- The earliest time to say Mussaf is Olot HaShachar, however, it should not be said before Shacharit.  If one said it before Shacharit one has fulfilled one’s obligation after the fact. 
- The latest time to finish Mussaf is the end of the seventh hour, however, if one didn’t say it before the seventh hour one should still say it before the end of the day and even though one is called ‘negligent’ for having delayed praying one still fulfills one’s obligation. 
- According to some one should pray mussaf without a minyan before the end of the seventh hour instead of praying with a minyan afterwards, while others argue that praying with a minyan is preferable. 
- There is no makeup (Tashlumin) if one forgot to pray or missed the time for Mussaf.  See also the Tashlumin page.
If one started Atta Chonen in Mussaf
- If one started the bracha of Atta Chonen or any other bracha of a weekday Shemona Esrei one should stop in the middle of the bracha and start with the text for Mussaf. 
- This is equally true for Shabbat Mussaf as it is for Rosh Chodesh, Yom Tov, or Yom Tov Sheni Mussaf. 
If one has the option to pray both Mincha and mussaf
- If one has the option to pray both Mincha and mussaf the one should say Mincha first and then Mussaf. 
- After the fact if one did say Mussaf before Mincha (when one had the option to say both) nonetheless one has fulfilled one’s obligation. 
- If there’s not enough time in the day to say both Mincha and Mussaf according to some one should say Mincha, while according to others one should say Mussaf  unless one intentionally didn’t pray until that time in which case everyone agrees that one should pray Mincha. 
- Some say that one only has to pray Mincha before Mussaf if one plans on praying both prayers now however if one plans on saying Mincha later then one may say Mussaf first , however, past nine and half hours one should always say Mincha first even if one plans to say it later. 
- A congregation should be careful to avoid this situation and finish Mincha before six and a half hours. 
- Some say that if the situation arises that a congregation must pray Mincha and Mussaf (past sixth and a half hours) that one should pray Mussaf first so as not to confuse the people and make them think that in general Mincha precedes Mussaf. 
- If one unintentionally missed Shacharit of Shabbat one must say Tashlumin at Mincha. If one is in the situation where he has the obligation to pray Mincha, Mussaf and Tashlumin for Shacharit one should say it in that order, first Mincha, then Mussaf, and then Tashlumin for Shacharit. 
- Once the time for Mussaf (from Olot HaShachar) it’s forbidden to eat a meal (more than a KeBaytzah of bread) before praying Mussaf, however, it’s permissible to have a KeBaytzah of bread or a lot of fruit. 
- The custom is to be lenient to permit eating even more than a Kabaytzah of baked Mezonot (cakes and cookies) before Mussaf after having made Kiddish. 
- If one does eat before Mussaf one must first do Kiddish and have a Revi'it of wine or eat a Kezayit of baked mezonot (cakes and cookies) in order to fulfill Kiddish. 
- Rambam (Tefillah 9:13-4) writes that mussaf of Shabbat, Yom Tov, Chol Hamoed, and Rosh Chodesh is said after shacharit. S"A 286:1 writes this halacha in regards to mussaf of Shabbat. Aruch Hashulchan 89:9 explains that chazal instituted mussaf on any day on which a korban was brought. See Gemara Brachot 26b which says that certainly chazal instituted tefillah in accordance with korbanot because mussaf there is no source for mussaf amongst the prayers of the avot but only in the korbanot.
- Who is obligated to say Mussaf? There’s a dispute in the Gemara Brachot 30a-b whether an individual is obligated or not and perhaps an individual is obligated but is exempted by the congregation in the city. Tosfot 30b s.v. Ein quoting Rabbenu Chananel, Rosh Brachot 4:21, and Rambam (Pirush Mishnayot Brachot 4:7 hold that an individual is obligated in Mussaf and is not exempted by the congregation in the city. This is codified by the Tur and S”A 286:2.
- Chazon Ovadia Shabbat part 2: page 204, Halichos Bas Yisrael volume II page 104. Even though Shut Rabbi Akiva Eiger 9 writes that since Mussaf was established in place of the korban mussaf which was brought by only men and therefore women aren't included in this obligation and Shulchan Aruch rules that women may not recite a beracha on a positive timebound mitzvah, Chacham Ovadia in Chazon Ovadia Shabbat part 2: page 204 rules that women may nevertheless recite mussaf since they would receive atonement from the offering of the mussaf just like men. Mishna Brurah 106:4 quotes the dispute between the Tzlach saying they're exempt and the Magen Giborim holding they're obligated.
- S”A 286:1.
- Background: What’s the earliest time to say Mussaf? Tosfot 26a s.v. Tefillah writes that the earliest time for Mussaf is Olot hashachar just like Shacharit and similar to the korban mussaf which could be brought right after the tamid korban. This is also implied by the Gemara Avoda Zara 3b which says that on Rosh Hashana one shouldn’t say mussaf alone in the first three hours of the day implying that the rest of the year one could say it even in the morning. If so, why is mussaf at the end of the Mishna? It’s not tadir like the others. Rabbenu Yonah 19a s.v. Tefillat says that even though Mussaf could be said all day it should be said after Shacharit (because of the concept of Tadir VeSheino Tadir-the more common takes precedence). The Rosh 4:1 agrees that mussaf could be said all day from the morning.
- Rama 286:1
- There’s a dispute between Rabbi Yehuda and Rabbanan as to the latest time for Mussaf. Rabbi Yehuda says the latest time is the end of the 7th hour and Rabbanan say one may pray until the end of the day. According to some versions, this can be found in the Mishna on 26a however, it’s certainly a dispute in the Brittah on 27b. The Tosfot 27a s.v. Tah Shema says that the version which deletes Rabbi Yehuda from the Mishna is correct and that shows that Rebbe didn’t hold like Rabbi Yehuda. The Rambam (Tefillah 3:5), Tur, and S”A 286:1 hold like Rabbanan that one could pray Mussaf all day. However, in Gemara Brachot 28a, Rabbi Yochanan says someone who prays mussaf after the 7th hour is called negligent for having delayed praying earlier. The Tur 286:1(2) codifies this and says that even though the halacha permits one to pray Mussaf the entire day, one may not delay saying it because the primary time is the first seven hours of the day. S”A 286:1 also rules that one may not delay it past the seventh hour but if one did one is called negligent but still fulfills one’s obligation. The Mishna Brurah 286:2 explains that one shouldn’t delay it past the seventh hour because that is the primary time the korban Mussaf was brought.
- Tefillah KeHilchata 3:56 quotes Zeh HaShulchan 286:1, Rav Wosner, and Chacham Ben Tzion Abba Shaul who say it’s preferable to pray by oneself early and Rav Elyashiv who says it’s preferable to pray with the minyan.
- S”A 108:6 and 286:1. Mishna Brurah 286:3 explains that since the Korban mussaf is mentioned in the tefillah of mussaf and there's no makeup for the korban mussaf, there's no makeup for mussaf.
- S"A 268:2, Kaf HaChaim 268:9, Kitzur S"A 76:19. See also Shabbat Davenings.
- Kaf HaChaim 268:10 quoting the Eliyah Rabba
- The Gemara Brachot 28a says that Rabbanan hold that if one has before him both Mincha and Mussaf one should say Mincha first because it’s the more common prayer (Tadir VeSheino Tadir, Tadir Kodem). However, Rabbi Yehuda argues that since the time for Mussaf is going to pass one should say Mussaf first (that is only according to his opinion that the latest time for Mussaf is the end of the 7th hour unlike Rabbanan who say Mussaf could be said all day.) Later in the gemara, Rabbi Yochanan rules like Rabbanan. The Rosh 4:8, Rambam (Tefillah 3:11), and Rif (Brachot 19a) rule like Rabbanan. This is the ruling of Tur and S”A 286:4.
- The Gemara Brachot 28a says that the reason we pray Mincha first is because it’s the more common prayer (Tadir VeSheino Tadir, Tadir Kodem). The Rashba (Brachot 28a s.v. Tanu Rabbanan) says that after the fact if one said Mussaf first one has fulfilled one’s obligation because the concept of putting the more common prayer first doesn’t invalidate something after the fact. [See also the Taz 108:10 who uses this regarding Tashlumin.] This is quoted by the Bet Yosef 286:4 and codified by the Rama 286:3. [This is also explained clearly by the Mishna Brurah 286:11 that the reason for the Rama is that the concept of putting the more common mitzvah first is only preferable but not absolutely necessary.] Yalkut Yosef (Tefillah vol 1 pg 551) rules like the Rama.
- The Magan Avraham 286:3 writes that if one is very close to the end of the day and there’s only time to pray either Mincha or Mussaf one should say Mussaf since there’s Tashlumin for Mincha but not for Mussaf. Kaf HaChaim 286:36 holds like the Magan Avrham. However, the Dagul Mirvavah (on Magan Avraham 286:3) argues that the Yerushalmi explicitly writes that certainly the opinion of Rabbanan to say Mincha first applies when there’s not enough time in the day to say both however if there’s enough time to say both it’s unclear that the Rabbanan ever said their opinion. Hagahot Rabbi Akiva Eiger (also on the Magan Avraham) tries to defend the Magan Avraham by saying that perhaps the Yerushalmi was speaking about a case where there was no option of Tashlumin such as if a person intentionally didn’t pray until that time or if one was an onen (first day mourner) and in that case the Magan Avraham’s logic doesn’t apply. The Mishna Brurah 286:13 quotes this dispute. [It seems that the Mishna Brurah sides with the Magan Avraham because he writes it as the anonymous first opinion and even adds that Rabbi Akiva Eiger defends it.] Yalkut Yosef (Tefillah vol 1 pg 551) rules like the Magan Avraham.
- Hagahot Rabbi Akiva Eiger on Magan Avraham 286:3
- Tosfot (Brachot 28a s.v. Halacha) quotes the Ri who says that one only has to pray Mincha before Mussaf if one plans on praying both at this time however if one plans to say Mincha later one may pray Mussaf now. However, the anonymous first opinion of Tosfot argues. The Rashba sides with the Ri (and infers it from the language of the Gemara) and quotes the Teshuvat Goanim which also agrees. The Rabbenu Yonah (Brachot 19a s.v. VeYesh) comes up with this same idea on his own. The Tur 286:3 quotes it as a dispute but then writes that the Rosh would pray by himself and leave the minyan in order to pray mussaf before the time for Mincha comes. The Bet Yosef 286:4 quotes all the above rishonim who hold like the Ri. The S”A 286:4 writes the simple halacha that Mincha precedes mussaf and then quotes the opinion of the Ri (implying that the halacha doesn’t follow the Ri).
- The Rabbenu Yonah 19a s.v. VeYesh writes that the Bavli holds that once the earliest time for Mincha (six and a half hours) arrives one should say Mincha before Mussaf against the Yerushalmi which says that only after nine and half hours does Mincha precede Mussaf. Then the Rabbenu Yonah continues to say the distinction of the Ri and concludes that even according to that idea once nine and half hours passes one must say Mincha first like the Yerushalmi (even though we don’t hold the Yerushalmi for the basic halacha). The Rosh (Brachot 4:8) also quotes the Yerushalmi. The Rama 286:4 rules like the Rabbenu Yonah.
- Kaf HaChaim 286:37
- The Rambam Tefillah 3:11 writes that there is an opinion who says that only an individual should say Mincha and then Mussaf however a congregation should say Mussaf first so as not to confuse the people. This is quoted in the Tur and S”A 286:4 as a individual opinion (implying that it is not followed as the basic halacha). However, the Kaf HaChaim 286:37 writes that if this case happens one may rely on the combination of the Ri and Rambam (and Arizal who holds that Kabbalistically it’s always better to pray Mussaf first) the congregation should say Mussaf first even if it’s past nine and a half hours.
- Yalkut Yosef (Tefillah vol 1 pg 551, Kitzur S”A 286:14)
- The Gemara Brachot 28b writes that the halacha doesn’t follow Rav Huna who says that it’s forbidden to taste any food before praying Mussaf. The Tur 286:3 writes that even though we don’t hold like Rav Huna we only permit have a snack but a meal is forbidden. The Bet Yosef quotes the Raavad, Rashba, and perhaps the Rabbenu Yerucham who agree. S”A 286:3 writes that it’s forbidden to eat a meal before praying Mussaf but it’s permissible to have a snack. The Magan Avraham 286:2 writes that the snack is the same as before Mincha where S”A 232:3 writes that one may have a KeBaytzah of bread and a lot of fruit but not more.
- Shaar HaTziyun 286:7 writes that the measure for a meal before mussaf in regards to baked mezonot is the same as by Sukkah. Mishna Brurah 639:15-6 (regarding Sukkah) quotes some who say that if one establishes a meal out of the Pas HaBah Bekisnin certainly it requires a Sukkah. However, if one didn’t have it as a meal if one had more than a KeBaytzah then there’s a dispute whether one needs a Sukkah and if one eats less than a KeBaytzah then certainly it doesn’t require a Sukkah. Nonetheless, Halichot Shlomo (Tefillah 14:9, pg 179-80) writes that the minhag is to lenient to have even more than a Kabaytzah of baked mezonot.
- Magan Avraham 286:1, Beiur Halacha 286:3 s.v. Achilat, Mishna Brurah 286:7, Shemirat Shabbat KeHilchata 52:17