Getting financial support in Grad school (from 'How to be a Good Grad Student')

Most graduate students (at least in the natural sciences) have a source of financial support that pays their tuition and a small living stipend. Although nobody ever got rich being a graduate student, you probably won't starve either. Sources of funding include fellowships (from NSF, universities, foundations, government agencies, and industry), employer support, research assistantships (i.e., money from a faculty member's research grant) and teaching assistantships.
Start looking for money early. Many schools arrange support in the form of an RA or TA position in the first year, but after that, you're on your own. Deadlines for applications vary, and if you miss one, you'll probably have to wait another year. After you apply, it can take six months or so to review the applications and several more months to actually start receiving money.
Ask faculty members (especially your advisor, who should be helping you to find support or providing support out of his or her grant money), department administrators, and fellow graduate students about available funding. Go to your university's fellowship office or its equivalent, and look through the listings in "The Annual Register of Grant Support", "The Grant Register", "The Chronicle of Higher Education", and "Foundation Grants to Individuals". Look into NSF grants (there are several different programs). Take advantage of your status as a woman or minority if you are one (this may be the only time when it actually is an advantage). Most universities have fellowship programs that may be administered through individual departments or may be campus-wide.
If you haven't yet begun actively doing research, getting an RA position from a faculty member may be a good way to become involved in a research project. Working on an existing research project by maintaining or developing hardware or software, writing reports, and running experiments will give you a feel for what it's like to do research -- and you may even find a thesis topic. Ask around to see what's available, and go talk to professors whose work you find interesting.
For a research grant or fellowship, you will probably have to write a proposal, so the more you've thought about potential thesis topics, the better off you'll be. You may need to tailor your proposal to the interests and needs of the particular funding agency or program you're applying to, but stick to something you know about and are sincerely interested in.
Write for a general audience, since the people reviewing your application may not be in the same field. Emphasize your goals and why the project you propose to work on is important. Talk as much as you can about how you're going to solve the problem, and be sure that your proposed solution will satisfy the goals you've set forth. Follow the rules for format, page layout and length, or your application may not even be reviewed.