The First Year
The First Year of your Ph.D. or M.S. program you will be taking classes and rotating through labs to find a good fit. If you are a GTA, you will also be teaching. Obviously, this is a very busy time and a lot is expected of you. You need to keep your grades up, devote a lot of time to teaching and every spare minute should be spent in the laboratory. The ability to multi-task will really help you out here. Do your homework or grading in the lab while you're waiting for restriction enzymes to digest. Also, take advantage of the Winter and Spring breaks to spend some uninterrupted time in the lab and make some real progress on your project. By the end of the Spring Semester you should have decided on a lab and be starting work on your thesis research.
The Second Year
You'll still be taking classes, but this year you should have more time to devote to research. You should be mastering techniques, and gathering an in-depth understanding of your chosen area by reading the literature and talking to your lab mates. You should identify the members of your Graduate Student Committee and meet with them to present and discuss your project plan. Towards the end of the second year (if you are in the PhD program) it's time to think about setting a date for the Preliminary Exam. The prelim must be taken by the end of the third year to qualify you as a Ph.D. candidate but it's best to get it done earlier. If you are in the MS program, by the end of the second year you should be beginning to wrap up your research project and starting to write your thesis. The MS degree usually takes between two and three years to complete.
The Third Year and Beyond
You should be done with most of your classes and spending every waking moment in the laboratory. Hone your scientific writing and presentation skills, stay on top of the literature and attend seminars and conferences. Take every opportunity to expand your experience. You will likely be considered a more senior member of the laboratory and may be required to train undergraduates and junior graduate students. See this as a chance to get experience that will be invaluable when managing your own lab and projects in the future. Annual committee meetings will encourage you to regularly evaluate the direction and progress of your project.
Your research should be complete within four or five years. Don't forget to start planning the next step of your career at least six months before graduation!