The amount of financial aid a student or family receives depends heavily on three factors: 1) the annual income and asset values of the family, 2) the price of tuition, and 3) the financial aid endowment of the school. Every offer of financial aid that you receive will be different because for every school, at least one of these factors will be different.

Depending on the endowment of the school, the amount the family/student will be expected to pay remains relatively constant. A lot of schools pledge to meet 100% of demonstrated need (from the FAFSA/CSS Profile), which means that they will subtract the amount you can contribute from their total cost and somehow account for the rest of the cost with financial aid. Of course, not all schools promise to meet 100% of demonstrated need, and many times these schools can fall far short of what the student/family actually needs.

Building from what cgrant45 said, if you're going to rely heavily on financial aid to finance your college education, you should apply to at least a few schools that make the 100% demonstrated need promise. This guarantees that you'll get at least what the government thinks you should get.