Register on time. Make sure you have no unpaid bills, especially tuition or library fines. These will sometimes delay registration. Submit all your paperwork before the deadline.
Ensure that you have completed the prerequisites for the class you want. If you are bypassing a prerequisite course, you will need the professor's permission to do so.
Find out your position on the waiting list by inquiring at the registrar.
Talk to the professor. If you make a good impression, the professor may be more inclined to help you. The prof always has the option to change his mind.
Be prepared for the prof’s questions. Express why you are interested in the course specifically. Explain that you feel you can learn the most in this particular class over another. Perhaps you are interested in pursuing a course of study in that specialty. If so, speak to it with passion. Explain that you appreciate professor's method. The professor wants to know that you’re interested in learning, not just in getting a good grade.
Ask about auditing. If the class is full, ask the prof if you can audit the class. Auditing typically means you attend the class every time it meets but you are not expected to complete assignments and you do not receive a grade. Find out from the prof what her policy is on auditing. Sometimes expressing a desire to audit is enough to show the prof you're serious about getting into the class.
Follow up. As the time draws near for the course to begin, check in again with the prof to see if any spots have opened up. Check in again after the course has started, as oftentimes some students will drop out in the first few weeks.