Several companies and organizations give away free books, including First Book, Kids Need to Read, the surplus books program of the Library of Congress, The Literacy Empowerment Foundation, the Books for Kids foundation, and the Scholastic Books grant program. Most of these free resources are made available to teachers.
Teachers, schools, and non-profit organizations can register and apply for a variety of grants and foundations to request books for their classrooms. These programs are often targeted to low-income or rural populations, where libraries are under-funded and students are generally under-resourced. First Book, for example, allows libraries, early childhood programs, faith-based organizations, schools, shelters, and after-school programs apply for new books and materials.
If you do not meet these qualifications, or you are looking for specific types of books, you may want to consider doing a book drive in your local community. To do this, you would simply visit various businesses or agencies and ask them to gather donations of new or gently used books. Providing them with a poster and a box for donations will help facilitate the process. After a period of a few weeks or one month, return to collect the books that have been donated. Don't forget to write a thank-you letter to each business or agency that participated in your book drive.
Another fun idea is having the children who received the books write thank-you notes or draw pictures for each business. Public recognition of the businesses or groups that participated is another helpful way to make the book drive mutually beneficial.