Order of Taking the Four Minim
Based on the pasuk ולקחתם לכם ביום הראשון פרי עץ הדר כפות תמרים וענף עץ עבות וערבי נחל "And you shall take on the first day the fruit of goodly trees, branches of palm-trees, and boughs of thick trees, and willows of the brook," we learn that we need to take one lulav, one etrog, three hadasim and two aravot.
Who is Obligated
- This mitzva of arba minim is an obligation on every individual. 
- Women are exempt from taking the arba minim because it is a mitzvah aseh shehazman grama. They are permitted and even encouraged to but while Ashkenaz women can say the beracha if they choose to do the mitzva, Sephardic women shouldn't say the beracha. 
- Women do not have to shake the lulav in all six directions as men do. 
- The obligation for children begins at the age when they can shake the lulav on their own.  When the reach that age, the father has an obligation to buy him a kosher set of arba minim that will be his own. 
- On the first day of Sukkot prior to shaking the lulav, we recite the beracha of ברוך אתה ה' אלוקינו מלך העולם אשר קדשנו במצותיו וצונו על נטילת לולב and add shehecheyanu. On the remaining days, including the second day of Yom Tov, we don't say shehecheyanu unless the first day was shabbat, in which case we would say it on the second day. 
- If one didn't take the four minim on the first day, then he says shehecheyanu the first time that he does. 
- The beracha and taking of the arba minim should be done while standing, but if you sat, you are yotzei bidieved. 
When to make the Bracha
- Since we are supposed to make the beracha before doing the mitzva (over liasiyatan)  and since we fulfill the mitzva of arba minim by simply lifting them together  it’s preferable to follow one of the following so that you say the beracha and then do the mitzva. Either
- take the Lulav, Hadasim, and Aravot in one’s right hand, leave the Etrog on the Table (out of the box) 
- or take the Lulav in one’s right hand, and Etrog in one’s left hand while the Etrog is upside down 
- or take the Lulav and Etrog in their upright positions and have in mind not to fulfill the mitzvah until you make the Bracha. and then make the Bracha. 
- After the fact if one took all four species (before making the Bracha), one may still make the Bracha as long as one didn’t shake it yet. 
Set up of the Arba Minim
- The Sephardic custom is to put one Hadas and one Aravah on the left of the lulav, one Hadas in the middle but slightly to the right , and one Hadas and one Aravah on the right side.  However, the Ashkenazic custom is to set up the Hadasim to the right of the Lulav and the Aravot to the left. 
- It is a mitzva to tie the lulav together, but if you don't it is still kosher. 
- Sephardim should tie the three together with lulav leaves in three places using double knots,  while Ashkenazim generally use the woven holder made of lulav leaves that has holes for the three minim, in addition to the three ties.  this holder is traditionally known as a keshetil.
- The minimum length for the lulav is four Tefachim, and the minimum length for hadasim and aravot is three Tefachim. There is no maximum length, however, if your hadasim or aravot are longer than 3 than your lulav has to remain at least a tefach taller so that at least part of it will shake recognizably. 
- One should make sure to tie it up so that the Hadasim are above the Aravot. 
- It is preferable not to have a non-jew tie them together for you, but if he does it is still kosher. 
How to Bind the 4 Minim (Eged)
- The halacha follows the opinion that it is not necessary to have the Lulav, Hadasim, and Aravot bound up together, however, it is a mitzvah and proper to do so to make the 4 minim look nicer.
- The Etrog is not tied up with the other 3 minim. It is held in the left hand while the others are held in the right hand.
- It is proper to bind the Lulav, Hadasim, and Aravot with a double knot. The Ashkenazic minhag is to allow using the kashekel's (woven lulav leaf holders) and consider them to be a binding of the 3 minim.For Sephardim, it is advised to tie the Lulav, Hadasim, and Aravot and not just use a holder.
- If one forgot and didn't tie them before the holiday, one shouldn't tie them with a knot on Yom Tov. Rather one should take a string, wrap them up, and tuck in the end of the string.
- If one didn't do so before Yom Tov, it is permitted to peel off a leaf of the Lulav to hold the minim together with a slip knot or winding them together and tucking in the end. The Ashkenazic minhag is to refrain from doing this except in private and in an abnormal fashion.
- If one forgot to tie the 3 minim before Yom Tov it is permitted to bind them with a pre-made lulav ring. However, it is forbidden to tie a lulav ring on Yom Tov. 
How to Hold Them
- We need to hold the arba minim right side up, "biderech gedeilatan"-the way which they grow.  The species shouldn't be turned downward when shaking in the downward direction, they should always be held upright and the shaking should be towards that direction.
- Holding the four species side-wise is incorrect.
- The Etrog should be held together with the other species at the bottom of lulav. Most hold that it is fine for the Etrog to be touching the hadasim and aravot and not directly touching the lulav spine.
- The minhag is that the spine of the lulav should be facing towards the person shaking it. 
- One should hold the lulav (aravot and hadasim included) in the right hand and the etrog in his left hand. 
- For people whose left hand is the stronger one,
- One should hold the arba minim against each other both for the holding and for the shaking. 
- It is prohibited to have something separating between your hands and the arba minim.  It is permitted to leave your ring on though or if you get hurt and need to wear a cast or a bandage that you can't remove it you can be lenient. 
Naanuim (Shaking of the Lulav)
- Sephardim shake the lulav before hallel when they first say the beracha and take the arba minim, then in hallel at the first hodu once, at anna hashem twice, and the second hodu once. 
- In addition to the times that sephardim shake, Ashkenazim have the custom that the chazzan shakes in yomru na also, and the congregation shake for all four hodu's that they say after the chazzan says his part, and the two hodus at the end of hallel. 
- Sephardim shake towards the south, north, east, up, down, west. (If the shul faces east then to your right, left, forward, up, down, backward.)  One should turn his body and face the direction to which he is shaking. 
- Ashkenazim shake east, south, west, north, up, down. Face forward and shake clockwise  You don't have to turn your body to face that direction, you can just shake the lulav towards that direction while facing forward. 
- One should refrain from shaking while mentioning the name of Hashem lest he become distracted while saying His name. 
- Some have the minhag to shake the lulav after reciting the bracha in the Sukkah.
Borrowing without Permission
- One may borrow a lulav and etrog without asking permission. Since it is a mitzva and the risk of damage is low, we can assume that the owner would allow it. However, if the one knows that the owner is meticulous about his, or circumstances dictate that he probably is such as it is meticulously wrapped or put away n a private locker, one should not use it without permission. This refers to the later days of Sukkot, However, on the first day (or first two outside of Israel) one does not fulfill his obligation with a borrowed lulav, even if it is with permission.
- Even a woman may borrow a lulav without permission, even though she is not obligated to do perform the mitzva, since she is permitted to volunteer.
- One should not borrow an etrog that is on sale, because the seller probably does not want them to be used.
- The arba minim don't retain their holiness after sukkot, but it still should not be treated disrespectfully like being thrown into the garbage. It is permissible though to leave them somewhere even if you know somebody else will throw them in the garbage. One who shows extra care by burying articles used for mitzvot, will receive beracha. 
- There are several other customs that people have to do with their arba minim. 
- Burn the lulav in the oven baking the matzas. 
- Burn the lulav on erev pesach with the chametz.
- Make etrog jelly and eat it on Tu B'shvat.
- Give the pitom of the etrog to a pregnant women as a prayer for an easy childbirth. 
- Use the hadasim as besamim for Havdalah. 
- sukka 34b based on Vayikra 23:40, Sefer Hachinuch Mitzva 324, Shulchan Aruch 651:1
- sukka 41b. Tosafot there says that since the pasuk says ולקחתם in the plural and not in the singular we know that it is on everyone.
- Mishna Sukkah 28, Shulchan Aruch 640:1. Like the other mitzvot aseh shehazman grama, if she wants to do the mitzva, she is permitted to. Ashkenazim based on Rabbeinu Tam quoted in Kiddushin 31b and Rosh Hashana 33a hold that women are permitted to say the beracha if they do the mitzva. Sephardim however, hold that they cannot say the beracha based on the Rambam in Hilchot Tzitzit 3:10 and Shulchan Aruch 17:2
- Shu"t Rav Pealim 1:12
- sukka 42a, Rambam Hilchot sukka 7:19. The Mishna Brurah 657:1 adds even if a child is six years old, the usual age of chinuch, if he cannot shake the lulav properly, one is not obligated to train him in this mitzva.
- Shulchan Aruch 657:1. Beiur Halacha there "kidei lichancho" adds that it must be kosher, and Iggerot Moshe OC 3:95 adds that it should be his own if possible.
- Hagahot Maimoniyot Brachot 11:3 writes there's no bracha on lulav the second day since we already did it yesterday but then he concludes that the minhag Ashkenaz was to recite it and the Rabbenu Peretz agreed.
- Shulchan Aruch 662:1-2.
- Mishna Brurah 662:3
- Chazon Ovadia 416 quoting the Shibbolei Haleket 366, and the Sefer Yereim 114 that its based on a gezeira shava learned from sefirat haomer. The halacha regarding sefirat haomer is in Rambam Hilchot Temidim Umusafim 7:23
- Pesachim 7b, Rambam Hilchot Lulav 7:6
- Sukka 42a
- As the rambam says in Hilchot sukka 7:5 the taking of the daled minim are all one mitzva and are miakev each other (meaning taking 3 without the 4th doesn't fulfill anything.) Therefore, until you take the etrog you haven't fulfilled your obligation, then you say the beracha, and then fulfill your obligation. The Bach 651 says that this option only works according to Rabbeinu Tam cited in Tosafot Sukkah 34b "Shetehei" who holds that one must take all four species simultaneously to fulfill his obligation. The Rosh Sukkah 3:14 disagrees and says there is no need to take all four together. Therefore, the Bach says this suggestion wouldn't work according to the Rosh. However, the Shaar Hatziyun 651:28 disagrees with the Bach and says even according to the Rosh this suggestion would work because even though you don't need to lift them simultaneously, you haven't fulfilled your obligation until you lift all four at least at some point.
- Holding the etrog upside down allows you not to fulfill your obligation until you flip it over because the gemara sukka 42a that in order to fulfill the mitzva of taking the daled minim all four have to be held kiderech gideilatan"-the way in which they grow. Mishna Brurah 652:16 says you aren't even yotze bidieved. Bach 651 (mentioned in the previous suggestion) says based on the aforementioned Rosh this suggestion would also not work unless you held all 4 minim upside down.
- This works because even if we say mitzvot don't need kavana (argument in Rosh Hashana 28b see http://halachipedia.com/index.php?title=Having_Kavana_for_Mitzvot ) to be yotze, most poskim agree that kavana not to be yotze doesn't fulfill your obligation. (Bet Yosef 589 and S”A 6:4). Rav Yosef Dov Soloveitchik in Reshimot Shiurim Sukkah 39a notes that this suggestion is only valid if over li'asiyatan requires one to recite the beracha prior to the fulfillment of the mitzvah but not if the beracha needs to be recited before the performance of the mitzva. Taz OC 651:5, writes that this suggestion is difficult as one may forget to have specific intent not to fulfill the mitzvah when he lifts them. However, this is the preferred method of the Biur Hagra 651:5.
- All three suggestions are made by tosafot in sukka 39a "over". S”A 651:5 suggests the first two suggestions, while the Mishna Brurah 651:25 quotes the Bet Yosef who brings the third option and quotes the Gra as saying that the third option is the most preferable. The Mishna Brurah makes no mention of which option is preferable. Yalkut Yosef (Kitzur S”A 651:14) also brings all three opinions and doesn’t decide on which is most preferable.
- Rosh sukka 3:33, Chayei Adam 148:11 Mishna Brurah 651:27 and Yalkut Yosef (Kitzur S”A 651:14). The Rabbeinu Nissim Sukka 20b "U'Midefarchinan" says that this is permitted even lechatchilah. The Bikkurei Yaakov 651:20 extends it to the entire hallel and the Aruch Hashulchan 651:14 says that as long as your still holding your lulav you can still say the beracha. Shaar Hatziyun 651:32 however rejects this opinion.
- Magen Avraham 651:4 quoting the Arizal writes that one should put one Hadas and one Aravah on the left of the lulav, one Hadas in the middle together with the Lulav, and one Hadas and one Aravah on the right side. The Shaar HaTziyun 651:11 quotes the Pri Megadim who says that one shouldn’t follow that practice unless one is known for his piety. However, Yalkut Yosef (Moadim pg 160, Sukkot p. 75) writes that the Sephardic custom is to follow the Arizal. The Chazon Ovadyah (Sukkot pg 343) also quotes the Magen Avraham.
- Mishna Brurah 651:12, Nitei Gavriel (Arba Minim 40:4). Mishna Brurah there adds that this is true for a lefty as well.
- Shulchan Aruch 651:1. Mishna Brurah 651:8 explains although we don't hold like the shita of Rabbi Yehuda on sukka 11b who says that you need to tie it together, there is still the mitzva of hiddur mitzva from the pasuk of זֶה אֵלִי וְאַנְוֵהוּ. Yalkut Yosef Moadim 159, Chazon Ovadia sukkot 340
- Shulchan Aruch 651:1, Chazon Ovadia sukkot 342 quotes the Sefer Yiraim 124 also and says that is the custom. He also quotes the Chatam Sofer sukka 36b as saying that since the mitzva of hiddur is objective based on what the torah told us, we should only use the double knots made of lulav leaves and not use the handles that they have nowadays. Mishna Brurah 651:14 quotes the Mordechai explaining that these three ties are representative of the three patriarchs
- Mishna Brurah 651:8 quoting the Shu"t Agura Biohalecha (12:273). Tzitz Eliezer 13:43 agrees to this as well.
- sukka 32b with Ritva, Ran, and Meiri there. Rambam Hilchot sukka 7:8 agrees too.
- Rama 651:1, Mishna Brurah 651:12, Nitei Gavriel 40:8, Chazon Ovadyah (Sukkot pg 343-4)
- Yalkut Yosef Moadim page 159
- Gemara Sukkah 33a cites a dispute between Rabbi Yehuda who holds that there is an obligation to bind the 3 minim together and the Rabbis who hold that it is only preferable in order to make the mitzvah nicer. Rambam (Lulav 7:4) and Shulchan Aruch 651:1 hold like the Rabbis.
- Rambam (Lulav 7:4), Shulchan Aruch 651:2, Yalkut Yosef 651:2
- Shulchan Aruch 651:1
- Mishna Brurah 651:8 citing the Agurah BeOhalecha. Bikkurei Yacov 651:8 writes that lulav rings as a binding is the equivalent of using a lulav kashekel.
- Yalkut Yosef 651:3
- Shulchan Aruch 651:1 writes that one may not tie a knot for the purposes of binding the 3 minim. See, the Chida (Moreh BeEtzbah n. 291) seems to say that there's no issue of making knots with lulav leaves. Kaf HaChaim 651:19 rejects this opinion. Yalkut Yosef 651:6 writes that if one didn't tie it before Yom Tov there's what to rely on to tie it with a double knot on Yom Tov.
- Tur and Rama 651:1, Yalkut Yosef 651:6
- Kaf HaChaim 651:20
- Shaarei Teshuva 651:3, Piskei Teshuvot 651:3
- Bikkurei Yacov 651:8
- Piskei Teshuvot 651:3
- sukka 45b. Mishna Brurah 652:16 and Chazon Ovadia Hilchot sukka page 340 say you aren't even yotze bidieved.
- Kaf Hachaim 651:47, Chazon Ovadia p. 341
- Chazon Ovadia p. 341
- Shaar Hakavaot 103b, Ben Ish Chai (Shana Rishona Haazinu n. 14), Kaf Hachaim 651:48. The picture of Rav Mordechai Eliyahu to the right as well as this video of Rav Ovadia Yosef (min 1:13) indicate that this is the correct way to hold the lulav and etrog. However, there is a Chabad minhag to hold the etrog at a slight degree away from the lulav but connected at the bottom (Sefer Haminhagim Chabad p. 66, Piskei Hasiddur dinei lulav fnt. 84).
- Nitai Gavriel 54:9 citing the Shaar HaKavanot 103b
- Chazon Ovadia Sukkot 358, Ben Ish Chai Haazinu 13 against the Eliyah Rabba 650 and the Orchot Chaim 23 quoting the Raavad who say that the spine should be facing away from him
- Shulchan Aruch 651:2. Mishna Brurah 15 explains that this is because the lulav, aravot, and hadasim have three parts of the mitzva while the etrog is only one.
- Tur 651, Shulchan Aruch 651:3. See Kaf Hachaim 651:38.
- Rama (quoting the Rosh 3:25 and Rabbeinu Yerucham) 651:3. Rama adds that if a lefty held it as if he were a righty, he is still yotzei. see however, Orchos Rabbeinu 2:pg. 288 that the Steipler who was a lefty and Ashkenazi, followed the Shulchan Aruch and not the Rama's ruling.
- Shulchan Aruch 651:11
- Beit Yosef 651 says for those who wear tefillin during chol hamoed remove it for the arba minim, although technically they don't have to because it doesn't cover the whole hand. Rama 651:7 paskins like this as well. The bach and the biurei hagra there however, both say that you must remove it because its considered a chatzitza as long as its not for the hiddur mitzva.
- Halichot Shlomo 224, Chazon Ovadia 417-419
- Even though the mishnah in sukka 37b doesn't mention any before hallel, Tosefot there "bihodu" adds that we should shake before also. Shulchan Aruch 651:8 and Chazon Ovadia sukkot 356 both agree to this.
- Rama 651:8 and Mishna Brurah 41.
- Chazon Ovadia 352-353 paskins like the Arizal against Shulchan Aruch 651:10 who says to start at east and turn clockwise.
- Bikkurei Yaakov 651:36 quoting the Ari as well as the Kaf Hachayim 651:96
- Mishna Brurah 651:47
- Mishna Brurah 651:37 quoting the Magen Avraham and the Maamar Mordechai.
- Mishna Brurah 651:37, Kaf Hachayim 651:84, Chazon Ovadia 655
- Rav Yitzchak Yosef (Motzei Shabbat Haazinu 5779 min. 6) explains that his father never took the lulav to shake it in the Sukkah.
- Rama 649:5 based on Terumat Hadeshen 100, Pri Megadim MZ 649:7, Halachos of Other People's Money pg. 66
- Halachos of Other People's Money pg. 67
- Shulchan Aruch 649:2, Halachos of Other People's Money pg. 67
- Halachos of Other People's Money pg. 66, Shu"t Igrot Moshe OC 2:106
- Halachos of Other People's Money pg. 67, Shu"t Igrot Moshe OC 2:107
- Mishna Brurah 21:6-7, OU.org, Star-K. Although the Shulchan Aruch 21:1, is referring to old tzitzit, Mishna Brurah 21:1 extends it to all items used for a mitzva including a lulav.
- Rama 21:1
- Most of these are based on Shabbat 117b which says that Rabbi Ami and Rabbi Asi would make a meal out of the bread used for the eruv, because it was already used for a mitzva.
- Rama 664:9
- Kaf Hachayim 664:60 mentions the last 3
- Tur 297 and Bach there.