I am a firstborn. Suppose I wake up late on Erev Pesach and walk into shul right after they finish the siyum. Can I still partake in the post-siyum meal, or am I too late? More precisely, what are the minimal requirements for breaking the Fast of the Firstborn?
I heard from a rabbi that it isn't strictly necessary to actually hear the siyum. The person who did the siyum celebrates by throwing a party and invites people to join him. All those that partake in the party are exempt from fasting.
In fact, some people mistakenly believe that hearing the siyum is all that's required, and subsequently go home to eat. This (according to the aforementioned rabbi) is a mistake. They must partake of the meal given at the site which celebrates the siyum.
The Gra, the shulchan aruch, and the mishnah berurah, all say you should fast.
The Gra was particularly insistent that healthy adult firstborn males should NOT get out of fasting on Erev Pesach by attending a siyum, but should actually fast! However, even the Gra conceded that, when Pesach starts on shabbos or motze shabbos, and the fast is pushed ahead to Thursday, since it is no longer done on Erev Pesach, one may attend a siyum to avoid the fast.
Wikipedia has an unusually erudite exposition on the fast of the firstborn, including a whole section on when/how to break it. http://en.wikipedia.org/wiki/Fast_of_the_Firstborn
If you miss the siyum, and you're otherwise healthy, just fast. After kiddush on the first cup of wine at the seder, you can have as much water and other food (except matzah and matzah meal products) as you like.
The main obligation is to give charity (and thereby "redeem the fast"). The siyum itself is really just extra, and in fact, as noted in the answers above, the siyum doesn't really "work" since most people do not actually join in a celebratory meal afterward. So the minimal requirement is charity. This was explained by one of the poskei hador in the US, R. Henkin
If a firstborn attending a siyum does not hear the completion of the tractate, or if he does not understand what he hears, or if he is in the shiva period of mourning and is thus forbidden from listening to the Torah material being taught, some authorities rule that subsequent eating would not qualify as a seudat mitzvah and he would therefore be forbidden to break his fast (Ben Ish Chai 1:96:25; Rabbi Shlomo Yosef Elyashiv, Siddur Pesach K'hilchaso, p. 168; Rabbi Ovadia Yosef, Chazon Ovadiah, p. 99).
Other authorities allow a firstborn to break his fast under such circumstances (Minchas Yitzchak 9:45; Teshuvos V'hanhagos 1:300, 2:210 in the name of Rabbi Yaakov Yisrael Kanievsky). The Minchas Yitzchak (ibid.) suggests that a firstborn in such a position should at least try to contribute to the siyum in some way, such as by sponsoring or helping to prepare the meal.
In order to break one's fast on a seudat mitzvah, many authorities rule that one must partake of at least a kotevet of food (around 1.5 to 2 oz.) or a melo lugmav of liquid (at least around 1.7 oz.) at the seudah (Minchas Yitzchak, ibid.; Chazon Ovadiah, ibid.; Teshuvos V'hanhagos, ibid.).
Other authorities rule that a firstborn need not eat anything at the siyum itself, and that he may break his fast anytime after the siyum (Siddur Pesach K'hilchaso, ibid; Rabbi Yehoshua Menachem Mendel Ehrenberg, Devar Yehoshua 2:81).
Additionally, the Mordechai (Pesachim 107) quotes the ruling of his father-in-law Rabbeinu Yechiel that firstborns need not fast at all on the day before Passover; firstborns need only limit their diet to snacks. (The Bigdei Yesha commentary suggests the rationale behind this ruling was to avoid holding a fast during the month of Nisan, which is generally prohibited.) The Mishnah Berurah states that it is appropriate for a weak individual to follow this ruling.
The opinion of R' Tz'vi Pesach Frank, regarding if someone made a siyum and did not fast on a Thursday adjusted fast, may also be of interest:
The above halakhic quandary is avoided completely if a firstborn fasts the entire day on Thursday. However, Rabbi Feinstein makes no mention of this requirement. In order for a firstborn (who eats on Thursday) to comply with the ruling of the Rema, the Piskei T'shuvot suggests participating in a second siyum on Friday, while Rabbi Tzvi Pesach Frank suggests partaking on Friday of leftovers from the previous day's siyum.