There are many different ways students are funded throughout their graduate career. Some faculty won't take students without having funds available or in the works. Others consider the student's likelihood of securing their own funding as part of the selection process. Some faculty don't take it into account at all. It's very important when you are talking with potential major professors that you understand their approach to graduate student funding.
Some faculty fund an incoming student within an existing grant.
This means the faculty provides a job for a new student or the new student agrees to perform the research as their own graduate project. Some students get fellowships during grad school. Unlike other schools, T.A. jobs aren't guaranteed because of the separation between the GGE and the departments. However, if you apply for TA positions by the departments' deadlines, you will get one.