Put all books to donate in a bag or bags. Flip through the books to check for damage --- if a book is missing pages or is excessively written in, avoid donating it to a Denver library.
Take all books in decent condition (torn covers are acceptable) to the Denver library nearest you. They accept most book donations. Call the Central Library at 720-865-1111 to find your local library, and ask about any current donation guidelines. Ask if they need any particular kind of book, then keep an eye out for it at used book stores for later donation.
Donate books to a Goodwill (303-650-7700), Salvation Army or other Denver thrift stores (see Resources). There are several of each, and they accept books, usually in any condition.
List your books on Freecycle after signing up on their website (see Resources). People list both free items and requests. Once someone responds who wants the book or books, arrange a time to meet up. This is a more personal method of donation because you'll know you're giving a book to someone who specifically wants it.
Donate educational and children's books to a Denver school. They can always use more age-appropriate reading material, even if they have copies already.