After you pick up skill books, go into the inventory, select them and use them. IIRC they go in the same category as potions and charms. After being read, you will have an additional skill point when you go into your skill list. You can read dragon skill books as a human, but would need to transform into a dragon in order to apply the extra skill point (you can read them as a dragon, as well, but you will get one or two dragon skill books before you have the ability to transform).
For quest books you just read them as you would any other book, but to achieve the desired result you may need certain ingredients (which it would mention) or it may need to be read at a specific location.
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