How do I get financial support to do a PhD?

You will not pay tuition to earn a PhD.  In fact, you will almost certainly get paid. In most cases, students do not incur additional debt while earning a Ph.D.

While you are getting a Ph.D. you are both an employee and a student of the university.  In return for the work you do on research projects (or as a teaching assistant), the university provides compensation in the form of tuition and a stipend to cover your living expenses. Your PhD program will include an offer of financial support along with their offer of admission. Types of financial support include teaching assistantships, research assistantships, and fellowships. 

There are also a few fellowships for Ph.D. students, such as the National Science Foundation’s Graduate Research Fellowship, the National Defense Science and Engineering (NDSEG) Fellowship, the Hertz Foundation Fellowship, and the CSGrad4US Fellowship. You must apply for these fellowships separately from your applications to Ph.D. programs. They are typically quite competitive and recognize student achievements.  

Fellowships are nice to have, and can give you more flexibility in choosing your advisor and research problem, but getting one usually doesn’t affect the amount of money you’ll receive while working towards your Ph.D.