Pick a graduate advisor that has expertise in your area of study or your research area. Graduate advisors with experience in your area of interest will have the best information and advice for you as you work on your graduate thesis. This will also ensure that your graduate advisor actually has interest in your field of study.
Choose an advisor who has a good reputation with other people in his or her field. If his peers do not look highly upon the advisor you chose, your work may not be looked upon highly either. Also, make sure that the graduate advisor you choose has a good reputation with other professors and students in your department. This will make it easier for you as you select a thesis committee and complete your thesis.
Consider the availability of the graduate advisor you choose. If a particular professor will take a sabbatical (time off) for a year during your studies, you may want to consider another graduate advisor who will be available for you. Also, be sure that the professor will be on campus for office hours or meetings when you need her.
Think about how well you get along with a prospective graduate advisor. Because you will work with your graduate advisor for at least several years, you will want to have a good working relationship with your graduate advisor. If you have had major disagreements with a professor in the past, consider another professor to work with. Furthermore, choose a graduate advisor that you respect and that respects you in return.
Choose a graduate advisor who has had proven success as an advisor. Ask yourself if the professor's former students have actually graduated in a reasonable amount of time. If a certain professor seems to have graduate advisees who don't graduate or who take a very long time to complete their theses, consider a different advisor. You want to choose a graduate advisor who has former students who have graduated in the recommended amount of time.