"Peel", "pare", and "skin"

I lately learnt these three words of similar meanings: peel, pare, and skin.

In what case do you use each of them? Could you give me example sentences along with a concise description for each?

While peel and skin are both nouns and verbs, pare is only a verb, from which I deduce you're talking about these words used as verbs. So:

• peel is primarily used for fruits and vegetables (peel an apple), as well as clothing (in the sense of removing: to peel off one’s pullover); it can also refer to other coverings on the surface of things
• skin is mainly used for persons, animals (skin the cat!) and fruits
• pare is, in my book, used much less frequently, but is as generic as skin

So, as I see it, skin is the most generic term, while peel refers mostly to fruits and vegetables (you probably wouldn't say you're peeling the cat). pare is much less used, but as broad as skin.

The meaning of those verbs is:

• pare: trim something by cutting away its outer edges; cut off the skin of something
• peel: remove the outer covering or skin from a fruit, vegetable, or shrimp
• skin: remove the skin from an animal, a fruit, or vegetable

Carlo pared his thumbnails with his knife.
Peel off the skins and thickly slice the potatoes.
He scrambled down from the tree with such haste that he skinned his knees.

_{[Reference: the New Oxford American Dictionary.]}