Skin is created whenever a creature without the [NOSKIN] Creature token is butchered.
When a skin is created a "Tan a raw hide" task will be automatically generated at a tanner's shop if Auto Tan is enabled and there is a Dwarf with the tanner labor enabled. He will then take the raw hide to the workshop and turn it into leather (or chitin, in some cases).
If left too long, a raw hide will rot and emit miasma, becoming useless. It may be a good idea to have a refuse stockpile near your tanner's shop which accepts only fresh raw hides if you plan to be butchering a large quantity of wild animals, so as to prevent your butcher's shop from becoming cluttered. If, however, you are planning to slaughter tame livestock, it may be even better to simply ensure that no stockpiles accept fresh raw hides so that they remain in the butcher's shop, since slaughtering always happens instantaneously and is not affected by clutter.
Make sure the tanner's shop is near the butcher's shop, since every second counts.