Hi there! Don't worry about having questions about financial aid, it's very confusing! I'm not certain how it works in psychology programs, but I have some experience with FAFSA in other graduate areas. You are able to receive a stipend and financial aid. They are two completely separate things. One (stipend) will be like a job and comes from the department, the other (financial aid) comes from the government.
The FAFSA for 2011-2012 just opened up on January 1. You can apply up until next April, 2012 for aid for the 2011-2012 year. However, you have a better opportunity of receiving grants (free money) rather than just loans if your application is completed by April 1, 2011. I actually recommend getting it done by March 1, because many things can go wrong. It helps to have that buffer month to get those glitches sorted out.
You'll go to
www.fafsa.gov, and follow the instructions there. You'll need to have your taxes and/or your parents' taxes, if they filed with you as a dependent, for 2010 completed in order to do the application. If you or they haven't done those yet, that's the first step!
You can choose up to 10 schools to which you want your FAFSA information to be sent. That way, you are in the schools' systems. Just because you send it to them doesn't mean you're going there, but it's easier to request scores be sent there now vs. later.
The likelihood of receiving aid depends on your EFC and the school's availability of funds. The EFC (Estimated Family Contribution) is the amount that the government determines you or your family can afford to pay towards your education in 2011-2012, based on your FAFSA application. This number will be the same, no matter what school you apply to. If you have a high EFC, you will be eligible for fewer funds, and a low EFC makes you eligible for more funds. Each school then subtracts your EFC from their estimated Cost of Attendance for one year based on your degree program and whether you will be full- or part-time. That final number is the amount you are technically eligible to receive in federal aid AND scholarships. Stipends, as I said before, are separate. I believe that fellowships are separate, too, but that might depend on the program and whether they process their fellowships as scholarships or stipends.
Different programs vary in the amount of aid they are provided from the government to distribute to their students. Generally, undergrads are eligible for more funds than graduate students, especially when it comes to grants. However, get your FAFSA done early in order to get the best shot at getting money!!
That's probably wayyyy more information than you wanted, but hopefully some of it is helpful!