I borrowed this list of tips on picking a tutor from another webpage

• If their poster looks unprofessional, that should be your first clue that something is wrong. [If you’re looking on Kijiji for a tutor, take note of any ads that have poor capitalization, grammar and spelling. If a tutor can’t take a few minutes to present his or her ad properly, can you really expect quality help from them?]
• If they sound like a weirdo on the phone, they will probably be a weirdo in person.
• If they offer a free intro session, you should not necessarily be impressed - if they are good, why would they need to offer free intro sessions?
• A good tutor is going to charge you from $20.00-$40.00 per hour but not all tutors who charge $40.00 per hour are worth that much!
• Level of education is not everything - someone with a BSc might be much better than someone with a PhD - you cannot tell until you meet them. [Sometimes people who are in a PhD program are there because the subject comes naturally to them. In that case, they may have trouble relating to someone, such as yourself, who is having difficulty with the subject.]
• If you cannot afford a tutor’s rate, try finding a friend to split the cost with and ask if you can bring a friend with you for tutoring sessions.
• If your tutor is rude, condescending, arrogant or fails to observe basic grooming (no I am not kidding), fire them and find someone else.

[Comments in brackets above are my own]
A few more:

• Ask your friends if they use a tutor. If your friend is happy with the person they’ve found, then you might have similar luck with the same tutor. Word of mouth is the best way to find a decent tutor.
• If your tutor isn’t helping, don’t be afraid to try someone new. Different people have different ways of explaining things and some tutors are more familiar with the courses than others.
• Find out if your tutor has actually taken the course you need help with (or, at least what his/her experience is in tutoring people in the course). There can be many ways to solve a problem and if your tutor isn’t familiar with the course, you may find the tutor teaching you things the long way!
• I personally have trouble with thick accents. If you do, too, avoid picking a tutor with a thick accent. Math (or whatever subject you’re getting help in) is hard enough without having to decipher an accent along the way.
• Ask your prof if they can recommend anyone. Often, they can suggest former students of theirs who have a good handle on the material.