Generally US higher education can be rather expensive compared to other university systems around the world. There are numerous ways to obtain financial aid.
At the graduate level, students can receive a full or partial tuition waiver and/or a stipend (money that they receive every month) if they work as teaching/research/service assistants. These kinds of opportunities are particularly available for PhD students. Assistant-ship positions vary from one institution to another in terms of financial benefits but the tasks are pretty much the same. The department chair is responsible for recruiting graduate assistants and generally knows in advance if the department has sufficient funds to hire graduate assistants. If you are interested in this option, you should contact this person immediately, once you apply to the program.
Most universities have two separate deadlines for application submission. One is called the financial deadline which is usually a little earlier than the regular deadline. By meeting the financial deadline, your application will not only be reviewed for admission but will also being considered for granting financial assistance.
Furthermore, some private US or international foundations offer merit or need-based scholarships to students corresponding to a particular profile.
A list of US institutions and private foundations offering financial aid to international students can be found at the following websites :