If you're planning to apply to graduate school, it's best to start early—it will increase your odds of being admitted. Many graduate programs have rolling admissions, which means applications are evaluated as they arrive (rather than all at once after the final deadline).
Here's a sample schedule for a student hoping to enter grad school in the fall. This is a best-case scenario which leaves time to craft a great application, resolve unforeseen problems (a lost transcript, a delinquent recommender) and submit with time to spare.
Begin researching potential schools . Take a practice GRE test. Your score will help you determine how much preparation you'll need for the real deal.
Request information from schools that interest you. Consider paying a visit to your alma mater to meet up with a few former professors. They can recommend good programs and may even help you make some connections.
Take the GRE general test. If you're not happy with your scores, sign up to take it again. Begin drafting your statement of purpose .
Register for the November GRE subject test (if necessary). Finalize your list of prospective schools, and familiarize yourself with the professors who share your research interests at each school. Contact your recommenders. Keep polishing your statement of purpose.
Request official transcripts from your undergraduate institution. Send your recommenders supplemental materials (like your resume, personal statement, etc.) that they can use as a reference. Make contact with students and professors at your prospective schools. Arrange a campus visit if you can.
Have someone in the field and a few smart (and honest) friends read over your personal statement. Take the GRE subject test; make sure that your scores will be sent directly to schools.
Complete and submit all applications, keeping copies of every section for your records. Verify that your recommendations have been sent.