Your best bet is to research the schools you’re interested in and look at what they offer in terms of assistantships. A good assistantship will cover tuition and provide a stipend. Assistantships generally come in three forms:
Research assistant (RA): As the name implies, the RA helps a professor with his/her research. Most of the time, only science departments offer RAships. Scholars in the humanities and social sciences primarily do research on their own, so they don’t need RA’s to help them.
Teaching assistant (TA): TA’s come in two varieties. The first type of TA independently teaches a lower level class of his/her own (although most TA’s spend a year training under a professor before assuming complete control of a classroom). The second type of TA doesn’t teach his/her own class. Instead, these TA’s assist the professor of record by proctoring exams, supervising lab sessions, and subbing in for the professor in his/her absence.
Graduate assistant (GA): A GA works in an administrative office. Most grad students hold GAships in their academic departments, but, depending on the school, a GA can also work in student services type positions in the admissions office or the library.
Resident Director (RD): An RD’s responsibilities include (but are not limited to) training RA’s, planning hall socials, and monitoring and disciplining the dorm residents. .
If you have applied to grad school and you didn’t get an assistantship, then don’t go, because an assistantship represents the department’s level of confidence in you. Ideally, the school should be willing to pay all or part of your tuition through an assistantship because they are duly impressed by your talents and want to recruit you as a scholar in training in their department.
With that said, it is possible to obtain other sources of funding, such as scholarships from your home institution, but these will be more limited and harder to get than an assistantship.
I hope I answered your question adequately. Feel free to leave a comment on my user page if you need any more help.