Financial aid is the key aspect of the application process for students applying to US Universities. The cost of attendance can be enormous without any funding. Financial aid can be obtained in the form of scholarships, fellowships, assistantships or student worker jobs.
Universities award fellowships and assistantships to top applicants. Most common types of assistantships are Research and Teaching assistantships. For assistantships, students need to work 20 hours per week. For many scholarships a separate application may be required. Many private organizations and foundations offer competitive scholarships - and one should apply for as many as possible.
To increase the chances of getting financial aid, the applicant should concentrate on all aspects of the application, including GRE scores, academic record and stetement of purpose. Research based programs offer more funding. Your statement of purpose should reflect a genuine interest in research. Any publication or paper presentation should be highlighted in your application.