Simplest form of sacrifice - some plant or thread or items. . . . a recycling mechanic when dorfs will sacrifice their worn clothes if replacement is available in your stockpiles or there is an abdurance of food.
Holy offerings shouldn't just be a slightly more flavorful variation on the atom smasher. The gods don't
want your damn X+llama wool sock+X. The word
sacrifice doesn't just mean stuff given to priests, it means a loss or hardship which is painful to endure. Temple sacrifices should be an outward show of inner devotion, and therefore they should be significant and meaningful.
Sacrifices should also be quite varied in their methods and manners, and appropriate to the relevant god's sphere(s) whenever possible.
It would probably be routine for every Grower who worships the god of Agriculture to tithe the first stack of crops that they harvest in every season. (These would probably be eaten raw by the priests in private, who would then store the seeds against emergency--if the fort ever runs out of seeds, it's only apropos that the church of Agriculture would "miraculously" provide them.)
A War deity would be pleased with an arena battle against captured enemies--provided that said enemies are armed & armored, NOT stripped naked & tied down.
A god of Youth might appreciate the gift of the very first bone bolts clumsily shaved by a dwarf who went on to become a Legendary Bone Carver. (The game has no way to identify such bolts at present, but one can dream.)
Worshipers of the god of Hospitality might maintain a shrine in the fort's Tavern, with a plate of good food replenished daily. This food would be free to visitors (although irreverent fort dwarves might also steal some).
The deity of Animals might like the gift of the fort's best stud Grizzly Bear, ritually slain after he's spent a couple of years impregnating the females--but when he also has several good years left in him, so the Animal Trainer who's donated him is actually losing something important.
Etc.