Start gathering information early.

Free information is readily available from:
High school counselors
College and career school financial aid offices (where you plan to attend)
Local and college libraries
U.S. Department of Education Web page
Other Internet sites (search terms student financial aid OR assistance)

Ask questions: counselors may know if you have exceptional circumstances that affect your eligibility.

Be organized: use calendars to keep on track.

Keep copies of all forms and correspondence: you must reapply for aid each year.

Parents of students: save money long before your child attends college.
College Savings Plan Network (state "Section 529" plans)
FinAid: for Parents
Tax incentives for higher education expenses

Good overviews:
Cash for College
FinAid: The Smart Student Guide to Financial Aid
Financial Aid: You Can Afford It
Looking for Student Aid
Mapping Your Future
Paying for College

Beware of scholarship scams -- don't pay for free information!
Department of Education
Federal Trade Commission