Join national organizations and apply for the grant money they offer to members. The Society of Children's Book Writers and Illustrators offers annual grants to writers. The Romantic Writers Association offers research grants.
Apply for art and writing grants through your local and state arts council. You can usually use these grants for anything that helps your writing project and they can fund writer in residence programs.
Search for grants to conferences and writing workshops you are interested in attending. Many conferences and workshops will have one or two grants that will cover the cost of a portion of the conference.
Look for organizations that support the research you are doing for your book. This is more effective if you are writing a non-fiction book. Professional organizations or endowment funds may provide grants to people who support their cause.