Find a mentor. Search the Internet for literacy councils and programs like UNESCO's, the National Institute for Literacy and literacy programs in your area. Read all you can about the programs they offer. Check pages that list their donors and funders. Verizon has a foundation that provides funding for literacy programs. If you check literacy program websites, you'll find them listed as donors repeatedly. Look for other foundations like that when cruising the literacy home pages and then find out how to get an application. You'll find them very polite.
Also, if you call your counterpart in another literacy program in another part of the country, they will very likely be more than happy to talk to you about what you want to do.
Get the straight poop on funding. There are regional, national and local nonprofit management centers whose entire job is to help you to figure out how to fund your charitable program. Many times, the local United Way or the public library will have lots of searchable information about what kinds of foundations support literacy programs. Make a list of not only national and statewide foundations, but also of all the dozens of local smaller foundations that give money for literacy programs.
Collect application forms from the foundations and government agencies you have identified. Write the applications. If you find the process intimidating, go to a grant writing class. They'll talk you through the process.
Submit the applications. You'd be surprised how many people write grants and never work up the courage to send them in. Will you get a no?
You bet! But don't take no for an answer. Make them tell you why and then fix it for next year's grant cycle.
Join a nonprofit social networking group like Virtual-Village.org. The membership is free and there are some successful literacy program mentors there who would love to talk you through the process.