When you apply for a PhD position, it’s likely that your main concern is whether or not they accept you, but you must also think about whether the supervisor is right for you.
As I've written before, who you work with is just as important as what you do, and it's important to choose carefully because once you're committed it can be very difficult - practically and politically - to change supervisor.
Although there's no way to know for certain before you start how your relationship with your supervisor will turn out, here are a few questions to ask them so you can get an idea.
What would you expect from me as a student, and what could I expect from you as a supervisor?
Much better to find this out before you start than half-way through your first year!
How many students do you supervise, and how often do you see them?
A meeting every 6 months is not enough. What is the point of having an experienced academic as a supervisor if you never get to benefit from that experience? I would say speaking to your supervisor once a month would be an absolute minimum.
It's also worth finding out how many other students they have, and what kind of interaction there is between students (are there research group meetings, for example). A good supervisor would encourage interaction among their students.
Is there funding available for conferences, publications and other research expenses?
Research is expensive. If you have to fund everything yourself then it will severely limit what you are able to do (publishing a paper in a peer-reviewed journal, for example, can cost thousands). Different PhD programmes have different amounts of funding for different purposes, and again it's good to find out what the situation is before you start.
Ask if you can speak to some of their current students
During my interview for a PhD position, I was introduced to one of the students who seemed to have a very positive opinion of the research group and the support and supervision he received. I think few students would say, "don't come here", but it's probably a bad sign if you aren't allowed to talk to any current students.
What's the best thing about being an academic?
You want to find out if they actually like their job. If they don't seem enthusiastic about their own work, they aren't likely to be enthusiastic about yours. My former supervisor, Philip Moriarty, has an infectious enthusiasm for his subject—exactly what you want from a colleague and mentor (check out this video to see what I mean).
Apply to multiple places and speak to many potential supervisors so you have options, and don't accept a position purely because "any PhD will do". Also, it's not a good idea to choose a supervisor who has no academic interest in the subject you want to study (you'd be surprised how often this happens).
Another potential problem is when supervisors leave or retire. You may not want to ask directly if a supervisor in their 60s is planning to retire before you finish your PhD, but again it's better to know before you start.