Find somewhere to donate locally. Most communities have libraries that are always in need of new books, and textbooks are welcome additions to any catalogs. There are also prison swap programs that provide textbooks to rehabilitated prisoners to read.
Find a global charity. If you cannot find a charity near you, there are plenty of global charities that are in need of used textbooks. Books for Children of the World and Books for Barrios focus more on children's and juvenile text books, but groups like The Global Book Exchange welcome college and adult-level books.
Send in your books. Whether you deliver them in person or through the mail, make sure your books get to their destination in one piece by wrapping them in plastic wrap or brown paper. This will minimize travel and damage that may occur. Write the name and subject of the book on any opaque covering.
Write off the book value in your taxes. Any valuable donation is tax deductible, so it pays to find out the current value of your books and then take proof of your donation (in the form of an invoice or receipt) to a tax professional to claim your donation on your taxes.