The Mishnah says in Masechet Zevachim, Perek Hei, Mishnah Zayin. Here we'll talk about the Shelamim offerings.
The Korban (offering) Shelamim is usually a voluntary korban that somebody brings, not to serve as any form of kapara (atonement) for sins, but it's brought by an individual who wants to have that feeling of being close to HaKadosh Baruch Hu, and sometimes it's also brought as a purification process.
The Shelamim offerings are considered to be Kodashim Kalim (offerings of lesser sanctity). They're slaughtered anywhere in the courtyard of the Beit HaMikdash, and the blood is applied to two different spots that become four. The blood is thrown on the northeast and the southwest corners of the Mizbeach (altar), and then it splashes onto all four sides.
The meat is eaten anywhere in the holy city of Yerushalayim by anybody; even non-Kohanim are allowed to partake of the Korban Shelamim. It's prepared in any way, and it's two days and one night. The day the Korban is offered, the following night, and the day after that, it's allowed to be consumed. And we said it's allowed to be eaten by anybody.
The person who brings the Korban gets most of the meat when it comes to Korban Shelamim. The Kohen (priest) gets another part of it. The Kohen gets the chest and the thigh, which is the thigh of the right hind leg; that's given over to the Kohanim. The parts that are given over to the Kohen, the chest and the thigh, are eaten in the same manner as the Korban itself.
The only exception is that, as opposed to the regular Korban, which is eaten by anybody, what’s separated off and given to the Kohen is only allowed to be eaten by the Kohanim, their wives, their children, and their slaves, their servants who work in their home.