Paying for Graduate School
There are at least four ways to pay for graduate school:
Once upon a time almost everyone was able to get funded by (1) the school, either with a fellowship, a research assistantship, or a teaching assistantship. All three generally pay your tuition and give you a living stipend of at least $1000/month. If you get a fellowship, they give you the money just because they think you are wonderful. If you get a research assistantship, you are getting the money for doing your research. A teaching assistantship requires that you assist with the teaching of some classes in order to get your money.
Now much of the departmental funding is reserved for Ph.D. students, and you may not have access to it as a Master's student. There are a lot of organizations that give fellowships for graduate school, and you should look into them. Obviously, paying for it yourself is somewhat less desireable than (1) or (2). (4) requires that you have a job at a company, and that they have a good policy on paying for graduate school.
Hertz Foundation fellowships is a prestigious fellowship which pays you $30K/yr plus tuition. Other competitive programs include the National Science Foundation's Graduate Research Fellowship and the SMART Scholarship. Notice that the deadlines for these are quite early. Because funding is tight for graduate school, a number of graduate schools have web pages listing fellowship opportunities, for example: Berkeley, CalTech, GaTech, Illinois, and Michigan.
If you know you are interested in a particular area, and if that area turns out to be a "hot topic" right now, you may be able to get fellowships/funding from special programs.