I picked my PhD supervisor when I was eight weeks pregnant, so ill and nauseated that I had to schedule all my meetings in the late afternoon (the time my so-called "morning sickness" had abated just enough that I could make it out of the house without guaranteeing that I'd vomit in public). I was sick, I was exhausted from the anti-nausea pills, I was completing coursework, and at the same time trying to figure out the next step in my PhD program.
You might think this was a bad place to be in terms of choosing a supervisor, but for me, the very reverse was the case. Being ill and inflexible had the glorious effect of making me focus only on the most important things while settling on a supervisor. Was s/he a good match for what would be my complicated schedule, particularly as I prepared for my candidacy? Would I be supported as I moved through the program, juggling my various professional and personal responsibilities? Did the way we both work match up?
Much of the literature on finding a PhD supervisor centres on other questions: questions of research interest and subject areas, and expertise in your field of choice. The advice often references those "star" researchers with international reputations who are constantly publishing and have an excellent reputation in their field. While these types of supervisors can indeed be excellent advisors, professors with strong research profiles do not by default make good advisors. In fact, the most important criteria for choosing your supervisor should not be the "star" criteria, but instead should focus on issues of compatibility. With that in mind, here are some tips for choosing a supervisor in your graduate degree:
1) Ensure your supervisor is interested in / has a strong investment in your work. Having a supervisor in your field is certainly a good idea, but sometimes you may find that for whatever reason--the interdisciplinarity of your work, your preferences in terms of work, their inflexible schedule, etc.--you need to choose someone slightly outside of your field. This can work swimmingly. Choose someone directly in your field to be your second or third reader on your committee, and your external examiner. Simply be sure that your supervisor thinks the work you are doing is valuable, insightful, and important, and can comment on it in critical and creative ways.
2) Know your work pattern, and try to match it with your supervisor's. I knew that I wanted a relatively hands-on supervisor who would read and comment on my draft work, could meet regularly, and would allow me to talk through some of my ideas while they were in process. One of my good friends, in contrast, wanted a hands-off supervisor who would allow her to submit completed chapters only, with little contact (pressure! she said) in between. These are two extremes, but they illustrate my point: figure out how you work, what you'd like or need in terms of a supervisor, and choose one who will complement and enhance your own work patterns. This can make a huge difference in terms of how you progress through the program.
3) Do your homework. Set up a meeting to talk to your potential supervisor about how they work, your own project, and if they would be interested in pursuing a supervisorial relationship. Did the meeting go well? Great! Do more follow-up. Ask around. Talk to other students that professor has had: Will s/he read and comment on your work in a reasonably, timely fashion? Does the student feel energized/encouraged by working with him/her? Does the supervisor have a good record of showing students through to completion? Of students who have found good jobs (in or outside academia, whatever your preference might be)? Take the time to ask former students and current ones about their supervisorial relationships, and then take more time to think about it. No need to rush the process, just do it thoroughly.
4) Try to find an advocate. The very best supervisors are those who are not only committed to your work and project but who also will have your back as you navigate the complicated and onerous bureaucracy of the university. I've been lucky to have a supervisor who has at least on two occasion written letters or attended meetings in order to represent my interests. You might not think this is important, but when you run up against what can be a dehumanizing and rigid system, you will be inestimably grateful that your supervisor can help you pierce through it.