Although one might think otherwise, the main purpose of a minyan is in order to allow for everyone in the congregation to recite the shemoneh esrei together in unison, a concept known as "tefilla b'tzibbur”. As we will see, however, it is not completely clear what exactly is considered to be reciting the shemoneh esrei together with the congregation.
There is some dispute as to the obligation, and importance of praying with a minyan. The Shulchan Aruch writes that “one should make an effort to pray with a minyan” leading many authorities to believe that praying with a minyan is optional in nature, or that one is not required to excessively inconvenience oneself in order to pray with a minyan. Other authorities argue that praying with a minyan is an outright obligation notwithstanding the seemingly discretionary nature of the Shulchan Aruch’s wording. In any event, we are taught that one who prays with a minyan is assured that his prayers will be received before God. One should go up to eighteen minutes out of one’s way in order to pray with a minyan. One is not required to suffer a financial loss in order to pray with a minyan.
According to all authorities, the ideal form of tefilla b’tzibbur is for the entire congregation to begin the shemoneh esrei simultaneously, following the lead of the shaliach tzibbur. One who is slightly behind the congregation in his prayers, and forced to begin his shemoneh esrei a few moments after the congregation, has still fulfilled tefilla b’tzibbur. If possible, however, one should try to begin the shemoneh esrei before most of the congregation would have reached “magen Avraham.”
Nevertheless, one who begins the shemoneh esrei while most others are still relatively within the beginning of their Shemoneh esrei, has fulfilled tefilla b’tzibbur. Other authorities argue that it makes no difference where the congregation is holding in their silent shemoneh esrei. According to this approach, one has discharged tefilla b'tzibbur as long as most of the congregation is still reciting the shemoneh esrei, regardless of where they are up to. So too, one who concludes the shemoneh esrei at about the same time as everyone else, also fulfills tefilla b'tzibbur no matter when one began it.
Some authorities allow one who requires extra time to recite the shemoneh esrei to begin reciting it before everyone else in order to ensure that one will be able to recite kedusha along with the congregation. Other sources seem to frown on such an arrangement and rule that one should never begin the shemoneh esrei before the congregation, even if it means forfeiting the opportunity to recite kedusha.
According to some authorities, one who arrives late to a minyan, or is otherwise behind in the prayers, should only begin the shemoneh esrei if one expects to finish it before the shaliach tzibbur reaches kedusha. Similarly, at maariv, one should only begin the shemoneh esrei if one expects to finish it before the shaliach tzibbur recites the concluding Kaddish. Other authorities dismiss these concerns and rule that one may begin one's shemoneh esrei at any time without worry about such considerations. One who is ready to recite the Shemoneh Esrei at the same time as the shaliach tzibbur is about to begin his repetition of the shemoneh esrei, should recite it along with him, word for word, if possible. In such a situation, one recites the kedusha along with the shaliach tzibbur, as well. One should also recite the abridged Birkat Kohanim (“Elokeinu V’elokei Avoteinu…”) that is recited daily in chutz la’aretz, and in Israel when no kohanim are present, along with the shaliach tzibbur.
Opinions differ whether there must be at least ten people reciting the shemoneh esrei together in order for their shemoneh esrei to be considered tefilla b'tzibbur or whether it suffices for just six out of ten to recite it together. While all authorities agree that it is ideal for at least ten people to recite the shemoneh esrei together, many authorities rule that it is still deemed to be tefilla b’tzibbur if even six out of ten recite it together. Similarly, most authorities rule that the shaliach tzibbur must wait until at least nine others have completed the shemoneh esrei before he may begin the repetition. According to others, however, it suffices for six people to have completed the shemoneh esrei in order to begin the repetition.
One who is unable to pray with a minyan should at least pray at the same time that the local congregation is scheduled to pray. If even this is not possible, it is preferable to pray alone in the synagogue rather than to pray alone at home. It is especially meritorious to be among the asara rishonim, the first ten, to arrive at the synagogue for a minyan. Most sources seem to rule that it is permitted to wake someone up so that they don’t miss a minyan. It is interesting to note that one who is hosting guests is exempt from having to pray with a minyan if one is busy tending to their needs.
 OC 90:9.
 Or L’tzion 2:7:8.
 See for example, Rambam, Hilchot Tefilla 8:1; Shulchan Aruch Harav, OC 90:17; Igrot Moshe, OC 2:27; Minchat Yitzchak 7:6; Teshuvot V’hanhagot 1:98.
 Berachot 8a; Meiri, Berachot 8a; Aruch Hashulchan, OC 90:13.
 Mishna Berura 90:52.
 Mishna Berura 90:29.
 Chayei Adam 19:1; Halichot Shlomo, Tefilla 8:7.
 Igrot Moshe, OC 3:4.
 Halichot Shlomo 8:7.
 Az Nidberu 8:41:4; Rivevot Ephraim 4:26.
 Piskei Teshuvot 90:14.
 Mishna Berura 66:35.
 Piskei Teshuvot 90:16; Yabia Omer 2:7.
 OC 90:10; Mishna Berura 90:34; Ben Ish Chai, Ki Tissa; Or L’tzion 2:87:5; Rivevot Ephraim 4:26, 4:27:8.
 OC 109:1; Taz, OC 109:1.
 Piskei Teshuvot 109:1; Az Nidberu 8:41.
 Rambam, Hilchot Tefilla 8:34; Teshuvot V'hanhagot 1:100; Refer to Rambam Hilchot Tefilla 8:34, Be’er Moshe 4:12; B’tzel Hachachma 4:3; Yabia Omer, OC 2:7.
 OC 109:2; Mishna Berura 90:14.
 OC 109:2; Igrot Moshe, OC 3:9; Be’er Moshe 4:12.
 Shevet Halevi 3:12:3.
 Chayei Adam 19:1; Teshuvot V'hanhagot 1:102.
 Rambam, Hilchot Tefilla 8:4; Magen Avraham 69:4; Shulchan Aruch Harav, OC 69:5; Kitzur Shulchan Aruch 15:7; Mishna Berura 69:8.
 Shulchan Aruch Harav, OC 55:7; Kitzur Shulchan Aruch 20:2; Kaf Hachaim, OC 55:48.
 Rambam, Hilchot Tefilla 8:4; Aruch Hashulchan, OC 55:13; Magen Avraham 55:8, 69:4; Shulchan Aruch Harav, OC 69:5; Mishna Berura 90:28; Minchat Yitzchak 9:6; Yechaveh Da’at 5:7; Beit Avi 3:24,4:2.
 OC 90:10; Kaf Hachaim, OC 90:64.
 OC 90:9.
 OC 90:19.
 Mishna Berura 55:34; Chayei Adam 67:11; Keren L’David18; Teshuvot V’hanhagot 2:50; Mishneh Halachot 12:443.
 Ahavat Chessed 3:1.