The Federal Pell Grant is for students with high financial need. Data from your FAFSA determines your Expected Family Contribution, or EFC, which is how much the government believes you can contribute towards college over one year. This is compared to your school's estimated Cost of Attendance, or COA. The lower your EFC, and the higher your COA, the more financial need the federal government calculates for you. As of 2010, Pell Grants are available for up to $5,550 per year.
The Academic Competitiveness Grant, or ACG, is available to Pell Grant recipients for their freshman and sophomore years of college. In order to be eligible, you must have attended a "rigorous secondary school program." Qualifications for such high school programs vary between states, and may include factors such as AP or IB testing. As of 2010, eligible students can receive up to $750 as freshmen and $1,300 as sophomores.
The FSEOG is reserved for students with the lowest EFCs, and priority is given to those with Pell Grants. Funding for the FSEOG is more limited than other grants, so the qualification process is more selective. If you believe that you may be eligible, turn in your financial aid documents early to ensure that you have the best chance to receive one. In the 2009-2010 school year, the FSEOG is available for up to $4,000 per year.
Unlike most federal grants, the National SMART Grant is only available to juniors and seniors enrolled in majors related to math, the sciences and certain foreign languages. As of 2010, eligible students must have a 3.0 grade point average (GPA) in their majors, and may receive up to $4,000 per year.
The TEACH Grant encourages students to enter elementary or secondary education after college. As of 2010, it is good for up to $4,000 per year, but recipients must take education classes and enter into contracts agreeing to teach for at least four years in low-income areas. If recipients do not fulfill this within eight years of graduating, then their grants will be converted into loans which they must repay to the federal government.
Not all grants come from the federal government---some are awarded at the state level, as well. For example, California has a program called the Cal Grant. As of 2010, Californian high school students can earn Cal Grants valued at up to about $9,700 per year if they submit their FAFSAs by March 2nd, meet minimum GPA requirements and attend a California college or university. Check to see if your state offers similar programs, and what their deadlines and requirements are.