For federal student loans, the limit depends on what year you are in and whether you're a dependent or independent student. For example, first-year undergraduate loans are available up to $5,500 for dependent students (up to $3,500 can be in subsidized loans). Independent graduate students can borrow up to $10,500 in their second year (no more than $4,500 can be in subsidized loans).
You can use the funds to pay for tuition, room and board and other school-related expenses. For more, read about college planning for parents or how to set a graduate school application timeline.