Know your limits and set goals for yourself before you start applying for funds. There are thousands of sources of funding for creative writers, each with its own set of requirements to receive funding. Know what you want to write so you can find a grant that suits your needs and not find yourself changing your writing goals to meet funding requirements.
Gather personal documents, writing samples and anything else that you might need to prepare grant proposals. Think about what characteristics make you unique or different from other writers. Write a personal statement and a schedule for completing the project, as well as a list of ideal publishers. All of this preparation will make the grant application process much easier to tackle.
Find as many sources of funding as you can. The National Endowment for the Arts offers fellowships for published writers every year, alternating between fiction and poetry. Look for funding at your state and local level as well, from organizations such as the New York Foundation for the Arts or local arts councils. National organizations like the Pen American Center for Writers is another source for funding. Applying for national foundation or NEA grants can be pretty competitive, however, so you may also want to narrow your search to find sources that are a close match to your goals.
Try to narrow your search for funding by looking for grants that match your goals, rather than casting a broad net. Think of specific key words that apply to your type of creative writing---and to your particular situation. If you are writing a coming-of-age novel set in the South, you might search for foundations that fund writers focused on that theme. Whatever you apply for, you'll have a better chance if your goals and the foundation's goals match up.
Read the instructions carefully and create a checklist to be sure you have all the supporting materials required to apply. Send writing samples that represent your best work or best represent the qualities that the "funder" is interested in. Send your applications in advance of the deadline. Keep a file of the grants you've applied for as well as a calendar of when award announcements will be made.