There is a wide range of methods for funding graduate study, from having your tuition paid and receiving a stipend and benefits all the way to paying completely out of pocket for tuition and living expenses. The biggest determinants of whether your schooling will be paid for are the degree program you are enrolled in and your field of study, but excellent candidates can find sources of funding even if they are not often given for that type of program. If your desired degree program does not typically pay tuition and give a stipend automatically, you should search out all the available scholarships and work opportunities that will help you fund your education.
If you are in a field where tuition remissions and stipends are typically given, vote with your feet by declining offers with sub-par stipends and/or benefits.
Tuition and qualified expenses are usually paid with scholarships, fellowships, employee benefits, out-of-pocket money, and/or loans.
Your living expenses are usually paid with fellowships, research assistant wages, teaching assistant wages, stipends, out-of-pocket money, and/or loans.
Further reading: Embrace Your Money-Making Options in Grad School