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One should be very careful to say Birchot HaTorah before learning. The brachot should be said with great Simcha (happiness) for being fortunate enough to be chosen and be privileged with the Torah. 
Before one learns Torah one must recite the Birchot HaTorah 
There is a dispute whether it is forbidden to learn Torah without brachot hatorah when one can't otherwise recite brachot.
The Text of the Brachot
The first bracha Ashkenazim conclude with the words “LaAsoak BeDivrei Torah” and Sephardim conclude with the words “Al Divrei Torah" 
The second section begins VeHaRev Nah with a Vav. Some Ashkenazim have the custom to say it without a Vav. 
When saying Birchot HaTorah especially “VeNehiyeh Anachnu VeTzeTzeynu” one should pray for one’s children to be Talmidei Chachamim, Tzaddikim, and Baalei Middot. 
The minhag is to say the Pesukim of Birkat Cohanim and the משניות of Elu Devarim after Birchot HaTorah. If one did not learn then, it is a dispute whether one fulfilled one’s obligation and so one should have intent to fulfill one’s obligation with the bracha of Ahava Rabba. 
There is a dispute whether the first bracha of Birchot HaTorah includes Haarev Nah or not. In light of this, there is a dispute whether one should answer Amen if one hears someone finish the bracha of LaAsok BeDivrei Torah, for Ashkenazim, or Al Divrei Torah, for Sephardim. Therefore, some advise saying this bracha quietly so that the listener will not be in doubt whether to answer Amen or not. 
One should be particularly careful about saying the Birchot HaTorah because they show one's appreciation of Hashem’s gift of Torah to the Jewish people. 
Some hold Birchot HaTorah are a Biblical Mitzvah and some consider it a Rabbinic institution. 
Someone who is in doubt as to whether they have already recited Birchot HaTorah, preferably should hear someone else make the brachot (the listener should have intent to be fulfilling his obligation by listening to the other person making the brachot and the speaker should have intent to fulfill his own as well as the listeners obligation by reciting the brachot), otherwise one should have intent to fulfill the obligation with the bracha of Ahavah Rabba or Ahavat Olam and learn right after davening. If that is not possible, according to Ashkenazim, one may make the bracha of the Asher Bacher Banu.  However, according to Sephardim, if one can not hear the bracha from someone else or have intent that one's bracha of Ahavat Olam fulfills one's obligation, one should not say the brachot.
One has to make Birchot HaTorah for any learning including Torah, Midrash, Mishna, and Gemara. 
Women are obligated in making the Birchot HaTorah. 
What Type of Learning Requires Birchot HaTorah?
Writing Torah even without reading, if one understands what one is writing, is considered learning for which one has to make Birchot HaTorah. 
According to Ashkenazim, because of a dispute one should not think Torah before making Birchot HaTorah, however it is permissible to do a Mitzvah even though it will cause one to think about the laws of the Mitzvah.  However, according to Sephardim thinking words of Torah does not require Birchot HaTorah and so it is permissible to think Torah before Birchat HaTorah. 
Hearing a speech of Divrei Torah from a person or an electronic device requires the brachot. 
Looking into a Sefer Kodesh and only reading with one’s eyes, even without saying the words, requires brachot. 
Telling someone a halacha without giving a reason is a dispute of the poskim, one should be strict to say Birchot HaTorah beforehand. 
One who hears a bracha may answer Amen before having recited these berachot themself. One also may answer Kedushah before reciting these brachot, even though the responses are themselves biblical verses. 
According to many poskim one may perform mitzvot without reciting birchot hatorah.
Someone Who Forgot to Make the Brachot
The bracha of Ahavat Olam (the second bracha of Birchot Kriyat Shema) exempts one’s obligation of Birchot HaTorah only if one learns immediately after tefillah. 
If one forgot whether one said the Birchot HaTorah (and had not yet said Ahavat Olam), Sephardim should not make a bracha, but Ashkenazim can make the Asher Bachar Banu bracha. 
Some say that one can interrupt between the brachot and the learning, but it is correct not to do so, and so the practice is the say the Parshat Birkat Cohanim right after the brachot. 
It is good to recite one's bracha out loud, to enable others to respond Amen. However, this is not an obligation. 
Interruptions That Would Require New Brachot
One who stops his learning by means of working, bathing, or sleeping, is not considered to have interrupted his learning and he does not make new brachot. 
If one slept during the day for a long period of time one does not make Birchot HaTorah again upon waking up. Even though there is what to rely on for one to make the brachot again, the Minhag HaOlam is not to do so, and one should instead hear them from someone who is obligated to make them (both must have kavana, and after the bracha, both learn some pesukim such as Parshat Birkat Cohanim). 
Women do not need to recite Birchot Hatorah multiple times a day.
The night goes after the day with regards to Birchot HaTorah; therefore, one does not make new Birchot HaTorah when night begins. However, if one goes to sleep at night, one will need to make new Birchot HaTorah when one wakes up..
If one woke up before Olot HaShachar (after Chatzot) and wants to learn, one should make Birchot HaTorah even if one will go to sleep afterwards. If one does go back to sleep Shinat Kevah during the night, there is what to rely on to make Birchot HaTorah a second time. 
Someone who wakes up early in the morning before dawn can make all the brachot (Birchot HaShachar and Birchot HaTorah) except Hanoten LeSachvi Binah and Parshat HaTamid which should wait until Or hayom. The Birchot HaTorah then covers his brachot all day. 
If one did not sleep all night, such as on the night of Shavuot, there is a dispute whether one should make Birchot HaTorah or not. According to Ashkenazim, one should try to hear the brachot from someone else, and then say some psukim afterwards. If one is unable to do that, one should have intent that one's bracha of Ahava Rabba should count for Birchot HaTorah, and then learn after tefillah. However, the Sephardic minhag is to say Birchot HaTorah by oneself.
If one slept Shinat Kevah the day before staying up all night, one should make the Birchot HaTorah in the morning after one did not sleep. 
If a person took a nap while in a chair leaning on his hands he doesn't recite new Birchot Hatorah when he wakes up and wants to learn. However, if he sleeps the entire night in a chair and that is normal for him, such as is common on an airplane, he can recite Birchot Hatorah anew after sleeping.
If someone goes to sleep on a bed at night even for a short period of time that would require new Birchot Hatorah. However, if he naps in his clothing in his bed some say that he doesn't need to recite new Birchot Hatorah while others disagree.
If someone went to sleep at night and got up to learn and is planning to go back to sleep afterwards should recite Birchot Hatorah when he woke up in the middle of the night as well as in the morning. However, some Ashkenazic poskim say that he should only recite Birchot Hatorah once in the morning and he is exempt when he woke up in the middle of the night from reciting Birchot Hatorah.
↑ Ramban in Sefer HaMitzvot of the Rambam adds Birkat HaTorah as a Mitzvah Deoraita based on Gemara Brachot which learns these brachot from the pasuk “Ki Shem Hashem Ekrah Havu Godel LeElokenu". See Ramban there and Minchat Chinuch 430:5 who classify these brachot as brachot of praise. Because of the dispute in the rishonim as to whether these brachot are Deoraita or Derabanan the rule of Safek Brachot LeHakel still applies.
↑Rav Nevinsal in Mishna Brurah 47:28 quotes Rav Shlomo Zalman and Chazon Ish who held that it is permitted to learn when one can't recite the brachot because of safek brachot lehakel. See Minchat Shlomo 91:1 s.v. agav.
↑ Shulchan Aruch 47:5 based on Rif (Brachot 5b), Rambam (Tefilah 7:10), Talmedei Rabbenu Yonah (Brachot 5b D”H Maiy Mevarech) and Arizal (Shaar Kavonot Nusach Hatefilah) have the version of Sephardim - Al Divrei Torah. Rosh (Brachot 1:13) and Tur 47 have the version of the Ashkenazim of LaAsoak BeDivrei Torah.
↑ Shulchan Aruch 47:6 based on Tosfot (Brachot 46a s.v. Kol, Ketubot 8a s.v. Shehakol in name of Rabbenu Tam), Rosh (Brachot 1:13), Rabbenu Yonah (5b s.v. Veha), Rashi 11b s.v. VeRabbi Yochanan, and Mordechai 31 hold that Harev Nah of Birchat HaTorah starts with a Vav. This opinion holds that really there are only two brachot of Birkat HaTorah. Rama 47:6 says that the practice is to say it without a Vav but it is better to say it with a Vav to satisfy all opinions. This opinion is sourced in the Rambam (Tefilah 7:10), Rashba (Brachot 11b s.v. VeRabbi Yochanan), Bal HaMor s.v. Maiym, and Avudraham pg 44. This opinion holds that Birkat HaTorah in reality consists of three brachot.
↑ Shulchan Aruch 47:6 rules that the bracha of HaRev Nah begins with the letter Vav to connect it to the last bracha. The Rama writes that though others hold that one should say it without a Vav, it is better to say it with a Vav. Magen Avraham 47:4 explains that the Vav shows that the first and following brachot are really one long bracha, and the opinion that the Rama quotes who argues that there should be no Vav holds that they are considered two separate brachot. Mishna Brurah 47:11 agrees.
↑ Shulchan Aruch 47:1. Gemara Nedarim 81a it is maintained that because the Jews did not say Birchot HaTorah the fist Bet HaMikdash and Israel was destroyed. The Bach 57:1 explains that their intention was to learn Torah just to learn the knowledge and be arrogant in their wisdom. They did not internalize the holiness of Torah into their body and soul and this caused Hashem’s Shechina to be removed.
↑ Shulchan Aruch 47:14, Magen Avraham 47:17 explains that it is because women have to learn the Halachot relevant to them. Minchat Chinuch 430:5 says that women can make these brachot because it is a praise of Hashem for giving us the Torah. The Gra 47:18 argues that women should not have to make the brachot since they are exempt from Torah learning. However he allows women to make the brachot like any other mitzvah from which women are exempt, Ashkenazic custom is to allow them to make a bracha.
↑ Shulchan Aruch 47:3 based on Avudraham (Birchot Hashachar beginning). Magen Avraham 47:1 adds that one has to understand what one is writing in order for it to be considered learning, but just copying over text is not learning. This is also the opinion of Biur Heitev 47:2.
↑Mishna Brurah 47:7 because of the Gra who argues on Shulchan Aruch.
↑ Shulchan Aruch 47:4 based on Shabbat 151a, Agur 2, and Tosfot 20b s.v. VeRav Chisda. This is also the opinion of Yalkut Yosef (vol 3 pg 81) that it is permissible to think Torah before Birchat HaTorah.
↑ Yalkut Yosef 47:5. Halichot Shlomo Tefillah 6:5 writes that certainly listening to a shiur requires birchot hatorah but listening to a recorded shiur might not. He explains that the mechanism of listening to a shiur being considered learning isn't based on Shomea Koneh. Rather it is based on the fact that it is original model of how learning Torah should be. That is, learning Torah involves a speaker and a listener and both are learning. See Tosfot Brachot 20b who seems to apply Shomea Koneh to Talmud Torah. See further the Machzik Bracha 47:4 who says that listening to a shiur requires birchot hatorah because of Shomea Koneh and has to answer why the Rosh, Tur and Shulchan Aruch O.C. 141 hold that Shomea Koneh doesn't work for Kriyat Hatorah. His answer is that the particular takana of kriyat hatorah excluded using Shomea Koneh. Dirshu 47:10 quotes Rav Chaim Kanievsky (Dirshu Gilyon 3) that listening to a shiur even on a recording requires birchat hatorah. His proof is Tosfot Brachot 20b that even if there's not someone speaking who is a person those listening are considered learning.
↑ Rama on Shulchan Aruch 47:4 based on Ran (Shabbat 4b s.v. Makom, Avoda Zara 19b s.v. Tana) allows this because it is just like thoughts of Torah. However Yalkut Yosef 47:7 rules that because of a double doubt one should be strict to make brachot.
↑Gra 47:10 writes that one may perform mitzvot without reciting Birchot Hatorah since thinking about them isn't done with the intention to learn. Mishna Brurah 47:7 follows the Gra. However, the Bikkurei Yakov 644:1 writes that before shaking the lulav one should recite birchot hatorah. (See Agur siman 1 cited by Bet Yosef 47:11 who writes that observing halacha in the bathroom prevents one from having an interruption for one's brachot hatorah since that is like learning. That implies observing halacha and certainly mitzvot is like learning. But the Biur Hagra 47 s.v. vhu hadin writes that the Agur is incorrect because observing mitzvot isn't learning. Also, see Biur Halacha 588:2 s.v. shma who suggests that thinking about mitzvot is like learning Torah with respect to learning in the bathroom.)
↑ Shulchan Aruch 47:7 based on Brachot 11b says that one can fulfill one's obligation of reciting the brachot with the bracha before Shema. Mishna Brurah 47:15 in name of Levush says that one can finish tefillah and it is not considered an interruption. Beiur Halacha s.v. Im Lamad implies from the Or Zaruh that finishing tefillah is ok but talking would be an interruption.
↑Sephardim do not make a bracha because it is a safek brachot lehakel since it is a dispute in the rishonim whether Birchot HaTorah are Deoritta (Ramban) or Derabanan (Rambam). This is also the opinion of (Yalkut Yosef Hilchot Pesukei DeZimrah 47:2 pg 60). Orchot Maran 5:6 writes that once when Rav Ovadia Yosef wasn't sure if he recited Birchot Hatorah asked him, Rav Dovid Yosef, to recite it for him. Ashkenazim can make the Asher Bachar Banu bracha as the Mishna Brurah 47:1 says in the name of the Shagat Aryeh.
↑ Shulchan Aruch 47:9. Tosfot Brachot 11b s.v. Shkevar in name of the Ri, Rabbenu Yonah 5b, and Mordechai 31 hold an interruption is not a problem. Rambam (as understood by Bet Yosef) holds one may not make an interruption. Magen Avraham 47:8 says that one can say these psukim even before daylight unlike the Maharshal who says one does not read psukim of Birkat Cohanim at night.
Tosfot Brachot 11a ask why a person does not need to make Birchat HaTorah again when they stop their learning and then go back to learning. The answer given, is that a person never gives up thinking about going back to learning because a person should learn whenever he has free time. The Rosh Brachot 1:13 and Hagahot Maimoniyot (Tefillah 7:9) agree.
The Agur (cited by Divrei Chamudot Brachot 1:76) explains that the reason there is no interruption when it comes to Birchat HaTorah is because a person is always involved in activities that require following halacha. The observance of halacha keeps a person’s mind connected to learning. Shulchan Aruch 47:10 holds that going to work or going to the bathroom is not considered an interruption and you do not therefore have to make Birchat HaTorah again.
↑ Shulchan Aruch 47:11 quotes those who say that a fixed sleep during the day is a hefsek, and then quotes those who say that it is not a hefsek; the minhag follows the latter view. However, Eliyah Rabba 47:9 quotes many poskim who say that one should make a bracha and agrees with them; Mishna Brurah 47:25 quotes many main acharonim who say to make Birchot HaTorah, and concludes that one who does will not lose out. However, many contemporary poskim including Piskei Teshuvot 47:14, Halichos Shlomo Tefilla ch. 6 fnt. 6, Rivevos Ephraim 8:609:1, Ishei Yisrael 6:25, Karna Deigrata 1:133, Halachically Speaking (vol 3, article 1, pg 5), and Piskei Teshuvot 47:14 write that the minhag is not to make any Birchot HaTorah after sleeping again in the day. Halichot Shlomo 6:2 writes that the minhag is that we don't recite new brachot hatorah after a daytime sleep. He explains that by doing so we indicate that the birchot hatorah aren't simply for the words of Torah but for the all encompassing obligation of learning Torah. Halichot Shlomo 6:3 writes that one shouldn't make a stipulation that one's birchot hatorah expire after one takes a nap. Even though it would be effective it is degrading the takana of chazal.
↑Tzlach Brachot 11b writes that since women aren’t obligated to learn Torah they should recite brachot hatorah every time they learn.
Bear Yakov 47:14 (Rav Chaim Krizer) writes that women don't need to make new brachot everytime they learn as long as they planned to learn more like the Magen Avraham says about men. Also, according to Rabbenu Tam it is a bracha of shevach so they don't have to recite it again.
Birchat Moshe Brachot v. 1 p. 232 Brachot 11b writes that really brachot hatorah are both birchot hodah and birchot hamitzvah. Therefore, women who are only reciting it for the aspect of hodah they only need to say it once a day. However, men who also recite it for a mitzvah might need to recite it again every time they learn. He also uses this to explain why chazal said everyone should recite the brachot if there's a chance that they might not learn that day at all and it'll be a bracha levatala (see Tosfot Ketubot 72a, Brachot 11b). Even if someone doesn't learn it is still a bracha of hodah.
Rivevot Efraim 5:43 quotes Rav Chaim Kanievsky, Rav Chaim Dovid Halevi, Halichot Bayta p. 20, and Halichot Bat Yisrael p. 118 who say that who do not need to make new brachot hatorah multiple times a day. Minchat Chen 1:4 and Halichot Shlomo 1:4 agree. Rav Shlomo Zalman explained it based on the fact that the women are cognizant of halacha all day.
↑Mishna Brurah 47:28, Rabbi Hershel Schachter (cited by Bet Yitzchak vol 30, p. 592). The side that says one should say it views Birchot HaTorah as similar to other Birchot HaShachar, which are said every morning, regardless of whether one slept or not.
↑Dirshu 47:25 quotes that Rav Shlomo Zalman and Chazon Ish held that going to sleep in one's clothing is shenat aray, Rav Elyashiv argued since it is in one's bed.
↑Mishna Brurah 47:29 writes that if a person went to sleep, got up to learn, and is planning on going back to sleep according to Rabbenu Tam once one made the bracha when he got up in the middle of the night he is exempt from reciting another bracha in the morning. However, according to most rishonim one should recite a bracha both times. He leaves it as one who recites the bracha doesn't lose anything. Similarly, Rav Nevinsal in Mishna Brurah 47:28 quotes Rav Shlomo Zalman Auerbach as holding that if one gets up in the middle of the night and goes back to sleep he should recite Birchot Hatorah twice, once in the middle of the night and once in the morning. However, Minchat Yitzchak 10:7 writes that one shouldn't recite Birchot Hatorah in the middle of the night except one should say it without Shem Umalchut. Then in the morning after one's primary sleep one should recite Birchot Hatorah.
Aruch Hashulchan 47:23 agrees with only saying it once but presents a compromise to determine when to say it. If a person woke up before Chatzot and is going to go back to sleep he shouldn't recite Birchot Hatorah, but he is woke up after Chatzot and is going to go back to sleep he should recite Birchot Hatorah. Aromemcha Elokay Hamelech p. 87 quotes Rav Tzvi Weber who agrees with the Aruch Hashulchan.