Find a graduate school that has a program in the field of study in which you are interested.
Visit the websites or call the graduate programs in which you are interested. Find out if the program offers graduate students jobs as research or teaching assistants. Many schools, especially large, public universities, hire graduate students to teach undergraduate classes or to help conduct research. The pay for these jobs may include tuition assistance, housing assistance, a stipend and even health insurance.
Contact the school and ask them to put you in touch with some current or former graduate students. Ask those students about the research or teaching assistant job and how the compensation matched their expenses. This will give you a realistic view of what is involved in the job as well as how well the payment will cover your expenses.
Familiarize yourself with the faculty in the graduate program to which you are interested in applying. If there is a professor whose research interests you, contact the professor directly and ask him about opportunities to work with him. Such personal contacts might facilitate your admission process and land you a research assistant job on top of that.
Choose your school and apply for the research or teaching assistant position you want. Be aware that the competition for these slots may be tough. Although some schools may offer all of their graduate students some type of assistant position. Teaching and research assistant positions are generally easier to find in fields of hard science, engineering and humanities.