I have looked at the different sacrifices described. Burnt, Fellowship, Sin, ext. Exactly how to perform the sacrifice is clear, and even the portions, but I don’t understand what happens to the meat. Short of the parts given to the temple, is the rest of the sacrifice eaten? or just burnt into the air?

There were many different types of sacrifices given on the many varied occasions (some obligatory, some voluntary). Some were totally burned, as if it were a gift to God; others have some portions burned and other specific portions eaten by the Kohanim; others have, in addition to the burned parts and those given to the Kohanim, also some specific portions eaten by the individual who brought the sacrifice and sometimes by his/her family and other specified friends, as well; and sometimes, specific portions could be eaten by anyone who was pure, even from outside the family. Everything is very exact and detailed.