From what I know, every Phd student needs to choose a supervisor in the first year. For someone who is entering a Phd with a broad interest in a field, this might be difficult since they don't immediately know what they want to work on. How do they go about choosing a supervisor in that case?
My advice will be similar to aeisimail's, and though I have not actually done exactly what I am suggesting, the main points are still based on personal experience.
(Also note that I come from the European setting (PhD in France currently) so the levels of education when you actually start looking for an adviser might differ, but I'll try to do my best to be general.)
In my opinion, there's three almost equally important parts to choosing what to do for PhD:
the subject (narrow field of focus, project you're taking on)
Even if you are not sure what exactly you want to do, if you don't see yourself getting at least a little bit excited about the subject, you will not be able to do it and enjoy it for the whole PhD duration. It also helps if you see the adviser being fascinated by what he does.
the adviser -- on both personal and professional level
Of course, you should read something about his previous works. Read some of his publications, something about ongoing projects. Ask around for information from other students. But also, if you have a chance, try and talk to the potential adviser, in person. Maybe some people can get a feel for an adviser from e-mail or other indirect communication, but for me, if I can hold an easy conversation with someone for 5-10 minutes, I'll probably be okay working with them.
the environment -- both for working and for living
If you can, try and get a feel for the research group and the lab you would potentially belong to. Depending on the type of person you are, you will prefer different environments. But, a friendly atmosphere is beneficial to everybody. Also, take a look at where you'll have to live (if you're moving for you PhD): a very extrovert person might suffer after moving to a small, quiet town. A big bustling town might overwhelm a shy and introvert person. Make sure you can be comfortable outside your PhD/job, because as much as you can't do a PhD if you don't love what you do, you won't be able to do it well if you don't like what your life is outside of that.
It might seem right now that you can survive with a good topic and adviser, in a bad environment, or some other way around, but think about it: those three things will be with you through the whole PhD. You can't do a PhD properly if you don't love what you do, who you do it with and where you are. All three of them are very important.
And some more specific advice that I collected over the years, which is probably not applicable in all the situations but is worth taking under consideration:
- young advisers at the start of their career are more likely to pay more attention to their students. If you want to work with your adviser, it will probably be harder with somebody who's already made a name for themselves: you're more likely to end up just working under them.
- the longer the people are in academia, the more they do administration instead of research. Know how to take advantage of what you have. If you end up with an adviser over his head in administration, keep research questions rare and to the point, when you need them. But know that these kind of people will be able to resolve some administrative problems for you that others might not be able to.
- no matter what type of adviser you get, in the end it is your own PhD topic. The adviser does not hold the absolute truth, and does not have all the answers. He's good for directing you and helping you focus, sometimes discussing problems, but towards the end of your PhD, you are the one that will become the foremost expert on the topic. Prepare for that, so you don't end up disappointed the first time you see your adviser guessing and struggling around your problem just like you.
- find what fascinated you about your own (potential) topic. Don't get all starry-eyed about what the output should be when looking for at a subject. If the output is all neat and useful and pretty, think about weather it has, for example, too much maths for you to be enjoying working on it. It's not just about what you are capable of doing, it's about what you enjoy doing.
Sorry for the short novel, I hope you find something that helps you.
Most research groups have seminars or weekly meetings. If you're not sure about a particular supervisor, but have a set of interests, try attending research group meetings for faculty in those areas. Faculty are quite used to this and will usually welcome the attendance (but do check with them first)
As it happens, your case was similar to mine—I didn't have a clue about exactly what I wanted to do, other than being interested in simulations rather than experiment. And, unlike JeffE's advice, in my field (chemical engineering), we don't get the option of working with multiple advisors for extended periods of time, because of the way project funding works.
What makes things easier for us? All of the faculty give presentations to the first-year graduate students, and all of the first-year students were required to meet with a number of potential advisors before ranking our preferences. This makes it easier, because we had to be active in seeking out advisors. Talking with graduate students in the group was also very helpful, because it allowed me to learn more about the advisors' styles, as well as the people that are in the groups. (Some of the groups were very cordial, others were not nearly so civil in their interactions—made a big difference in making my decision.)
When searching for a supervisor, look at their research profile (usually on a university website), paying particular attention to their fields of expertise/interests - look at and read any papers that they have had published and the nature of the PhD projects that they have already/are currently supervising.
Discuss what options there are with members of the Faculty that whose general fields you are interested in. Ask what projects are upcoming.
Hope this helps.
Pick someone at random. (Use your research interests and experience, and the available faculty's research interests and experience, to bias your probability distribution.) Work with them for a semester. If you both like the work that you're doing together, and they're willing to take you on as a student, you're done. Otherwise, repeat.
No, I'm not joking.
The ideal PhD supervisor has/provides:
A good track record of successful PhD students
Expert Knowledge and High Reputation
Sufficient Time for your PhD supervision
Opportunities for collaborations
A permanent and stable position
Sufficient, Secure, and Flexible Funding
Good office space
A position at a reputable university
Additional Mentorship Skills