The GRE has two tests. The General exam covers verbal, mathematical, and analytical ability, and is required for most schools. The Subject exam is in Psychology, and requires you to have good understanding of experimental and social psychology. The GRE is one of the most important parts of your application. The GRE is given world-wide.
Students usually take it during fall quarter of their senior year.
Generally, you will need 3 confidential letters, and they should be from faculty who know you well. This is especially important for competitive programs. You will want to approach faculty very early, well before you apply, and ask them if they would be willing to write strong letters of recommendation for you. These faculty should know you from courses and research. Faculty letters generally state how well you performed in class, performance in research, and will assess your ability to succeed in graduate school.