The amount of your financial aid package will be equal to:
Estimated Expenses - Expected Family Contribution.
Estimated expenses is a number each school determines. It is their estimate of what you total cost of attending school will be for the 9 month school year. It includes tuition, fees, books, food, housing, and misc expenses. The school's financial aid office can tell you exactly what this number is.
Here is an example from my former school, the University of Oregon:
Resident Tuition and Fees - 4875
Housing and food - 6570
Books and Supplies - 900
Personal Expenses - 2350
Total: 14,695
So if your EFC was zero, you should get a financial aid package of grants and loans totalling 14,695.
However, you have to be in a certain income group to receive certain grants and the availability and type of grants may vary from school to school. Normally, you would be offered federal loans(Stafford/Direct Loans and Perkins Loans) on top of any grants to get your package to 14695. But there are limits on the amounts these loans can be, so you may not always get the full amount of aid you are supposedly eligible for.
The yearly maximum for Perkins loans is 3,000
Yearly maximums for Federal Stafford Loans are:
Undergraduate - Dependent - Independent
First year
(1-44 credits) - 2,625 - 6,625
Second year
(45-89 credits) - 3,500 - 7,500
Beyond 89 credits
(total per year) - 5,500 - 10,500
Maximum allowed - 23,000 - 46,000