You need a specific potion for the animal/monster you want to tame. The way to obtain the crafting of those potions is different for each of them.
And what do I do with them
you do the nasty with them
you can feed them so they like you more and do random stuff like pet certain enemies, or fuck around and let them pound you or pound them. if you have enough dominance in one you can get a couple variations for them too!