First thing to note is the distinction between hides which create leather and pelts which give you fur. Once you get your hide or pelt, you want to cure it with some saline or salt water and just a little bit of cooking skill. The cured hides/pelts can now be stored until you learn tanning, which is a bit more involved and requires higher skill levels in cooking and/or survival or just a book with the recipe. Once you’ve got the recipe in your crafting menu, you just need to find all the required items. Big spoilers here, but this link tells you absolutely everything you need to know, what books to look for, what skills are required and all of the necessary ingredients. http://cdda.estilofusion.com/tanning_pelt/craft
Tanning pelts for fur is also far more useful, since leather can be easily found all over the place in huge quantities.