After filing your FAFSA form and getting accepted by your choice institution, you'll want to proceed by coordinating your financial aid efforts with your chosen law school's financial aid office. Visit sooner rather than later -- before other students snap up all the available money. Advisers at the office can tell you what types of aid you're eligible for, what the deadlines are and if you need to fill out any forms beyond the standard FAFSA form. It's good to get some idea of what you're getting into, so ask questions about their average graduate's loan debt and starting salary range.
While some lucky students will end up getting all of the money they need upfront through their schools (and it should be noted that some law schools are more generous than others, which could be a factor in your school selection process), the rest must usually turn to means besides grants and scholarships to cover the cost; namely, loans that eventually have to be paid back. When it comes to loans, there are typically two primary sources -- federal and private. You might very well end up having to make use of both.
For more details, read How Student Loans Work.
On the next page are links to lots more information about the steps for becoming a lawyer -- and about paying off the mountain of debt that may come with it.