Match the interests about which you are passionate with an adviser. Universities require their professors to participate in research throughout their terms as teachers. Reading the current and past research works of potential Ph.D. advisers exposes their voice and opinions on scientific matters. It is not necessary for you to agree with every opinion a professor has, but understand and appreciate his thought process. Also read books or non-research-oriented material that potential advisers published.
Learn whether or not the professor you want as your adviser will accept new advisee students in the upcoming school year. Ask his current Ph.D. students to find out. Contacting other students is less formal than contacting a professor directly but still allows you to gather useful information about the potential adviser.
Discuss temperament of potential advisers with their current or former Ph.D. students. Former students typically are credited with helping in previous research with professors. Advisers and their advisees often collaborate on research. Contact several past students to discuss their experiences with the adviser. Ask specific questions about personality conflicts and work-related opinions that may become issues as you progress through the Ph.D. program and develop strong beliefs about research you perform.
Contact the school secretary to set up an appointment to meet with a potential Ph.D. adviser. The secretary will know which days the adviser has time for students and if she will meet with a new advisees. It is not necessary to contact the professor directly; working through the professor's secretary shows respect for the professor's time commitments. When visiting with the potential adviser, arrive on time and write down a list of potential questions regarding advising and research. A personal meeting allows both the adviser and advisee to discover whether or not their expectations and goals are compatible.
Ask to work with the adviser. If funding or time constraints cause the adviser to deny working with new students, offer to apply for fellowships to make the partnership work. Be persistent but respectful in all interactions between you and the potential adviser. It may take a semester or two of persistence, but finding and working with the adviser of your choice will benefit you and your progress in the Ph.D. program.