In order to obtain your I-20 and student visa, I believe you have to demonstrate that you have sufficient funds available to cover your tuition fees, living expenses, etc. (e.g., savings/student loans, stipend + tuition remission, or fellowship)
I'm not sure how it works for unfunded programs, but for funded programs you are able to obtain a SSN and work authorization for paid work related to your program of study (e.g., graduate research assistant, clinical placement, etc.), but you are *not* permitted to take additional employment outside the university.
Work authorization is generally difficult or impossible to obtain for work unrelated to your program of study unless you can demonstrate financial need (but since you needed to demonstrate adequate support to get your I-20 in the first place, this is difficult to do).
The international student office at your university will be able to give you the details.