When animals are killed, their carcass can be skinned before being cut for meat. You do this by using the "Hideworking" skill menu (ALT+k) to skin an animal, then butcher for meat. The skin first acquired is fresh, but spoils in a few days, unless cured or tanned. Curing extends its lifetime. But tanning is much more useful, turning the skin into leather or fur, depending on the animal the skin comes from.

Animals that yield leather are cows, pigs, dogs, black grouse, and snakes.

These animal's skins become furs when tanned: Sheep, Bear, Badger, Glutton, Beaver, Reindeer, (Artic) Fox, Elk, Wolf, Lynx, Polecat, Weasel, Pine-marten, Hare, Ermine, Squirrel. However, if leather is desired, the skins can be de-haired after cleaning and then the tanning process continued as usual to yield leather.