Take the GRE in the winter of your junior year or the summer before your senior year or in October. You can plan your applications based on your scores. ETS keeps scores for five years so even if you don't plan on going right away, you might want to take the test while things are still fresh in your mind. Get information about the GRE's and application forms in the Career Services Office. Finances frequently restict the number of applications you will submit.
Most schools require an application fee.
Unless you are absolutely sure you want to stop at the M.A., always apply for the Ph.D. Schools take M.A. applications less seriously for both admission and financial aid. The M.A.T. combines intensive work in a subject area with Education course work and practice teaching. The former should be the best paper you ever wrote. And don't be afraid to make it better. Take it back to your professor and re-write it.