Eligible libraries should be in a rural area, have a limited operating budget (usually less than $40,000) and serve a population under 10,000. The guidelines and application can be found here: http://www.librifoundation.org/apps.html.
The Foundation will match any amount of money raised by your local sponsors from $50 to $350 on a 2-to-1 ratio. Thus, your library could receive up to $1,050 worth of new children’s books (about 70 books). Local sponsors have five months (or longer, if necessary) after their library has been selected as a participant in the Books for Children program to raise the matching funds. Deadline: April 15th.