Apply to the right schools. Many graduate programs will guarantee at least some funding for new grad students, while some will guarantee full funding. Investigate many schools and try to apply only to programs that will at least guarantee partial funding in the form of assistantships, grants or scholarships.
Become a teaching assistant, or TA. Even if you are not accepted for your first year, try again your second year. In the meantime, make strong contacts with professors who might want you as their TA and get good grades. The benefits of becoming a TA are health insurance support, tuition payment and an additional salary that varies from school to school but that will cover at least some of your living expenses. Also, this job will look great on future job applications.
Apply for scholarships. Scholarships are out there for just about anyone in any field. As early as possible, become familiar with what your school offers, as well as doing a general search for scholarships offered by various foundations, and apply for more than one. If you can do some community service before applying, that may help. Some scholarships might require you to write an essay, while others are specifically for students with a specific background. Even though some scholarships are for the academically gifted, this will not be the case for all of them, so examine your options carefully.
Look for on-campus employment. If you qualify for a work-study program, check out the available jobs as soon as you can, as some on-campus jobs are better than others. Check the bulletin boards regularly. For any employment opportunity in general, whether on campus or off, keep your grades up and develop strong relationships with your professors so that you can use them as references. Professors may also be able to recommend employment opportunities specifically for someone in your field of study. Keep in mind that many graduate classes are night classes and can accommodate work schedules.
See if your employer will pay for classes. Many companies offer full or partial tuition reimbursement, particularly if what you are studying is at all related to your job. It may take you longer to complete your graduate degree while still working full-time, but avoiding a mountain of post-graduate debt will make it worthwhile.
Create a budget and eliminate all unnecessary spending. Think about taking your coffee in an insulated mug versus buying it daily and packing a lunch rather than grabbing something from a campus eatery. If you can tolerate a roommate, get a roommate to help pay the bills. Live with family if that is a possibility. Buy used books or rent them. Even if you feel deprived by cost-cutting measures, realize it's a temporary deprivation you can endure until you reach your goal.