Since graduate schools are involved in intensive research, they usually receive funding from governmental grants and private donations. Receiving a research fellowship is very competitive. You must first be accepted by the graduate school. If you are considering graduate school , start at the end of your junior year by reviewing graduate programs and searching for fellowships on the web. Take your GRE's early and apply for fellowships and graduate school entry in the fall of your senior year.
Most universities have their own funded fellowship program.