There are a number of different types of offerings, brought for different purposes. Each one had its own details, but each detail is not an independent mitzvah. Rather, it is a mitzvah to offer the appropriate type of sacrifice following the prescribed procedure. (An analogy: if I tell my son to pick me up at the airport, “pick me up” includes “don’t speed,” “signal,” “check your mirrors,” etc. But all those things are part of “pick me up,” not separate items on his to-do list. If he gets in a fender bender en route because he’s speeding, not signaling and/or not checking his mirrors, I will say, “I’ll asked you to do one simple thing!” not “I asked you to do 47 discrete acts, of which you successfully accomplished 42…”)
The burnt offering is called a korban olah in Hebrew, so named because it was completely burned on the altar and “olah” means to ascend. A korban olah was brought for a number of reasons, including as atonement for sins that did not have reparations specified. The korban olah discussed in parshas Vayikra could be brought from any unblemished, male, kosher herd animal: bulls, sheep or goats. Pigeons or doves could also be used.
The animal could be sacrificed even by a non-kohein but after that, the kohanim would take over. As mentioned, this sacrifice was completely burned, including its hide, wool (if a sheep), bones, etc., so long as they remained attached to the animal. The feathers were burned with the birds.
The reason underlying sacrifices is to bring us closer to God. We’re far removed from such offerings, so it’s hard for us to understand. One way of looking at it is that, really, we are culpable and deserving of such treatment but God, in His mercy, allows us to bring sacrifices as a surrogate. Even so, this is hard for many people to reconcile with contemporary sensibilities. For now, suffice it to say that the Torah permits us to use animals, but not to gratuitously abuse them. We see the Torah’s concern for the needless suffering of animals in many places. Clearly, sacrifices served a lofty purpose or they would not have been permitted.
The obligation to properly offer burnt sacrifices applies to male kohanim when the Temple is standing. It is discussed in the Talmudic tractates of Zevachim (53b), as well as in Tamid and elsewhere. It is codified in the Mishneh Torah in chapter 7 of Hilchos Maaseh HaKarbonos and is #63 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.