Hi all. I'm in this court-ordered psychotherapy, so this doesn't really apply to me, but since I'm a graduate student in Psychology, I thought I might have something useful to say.
1. Get recommendations. Ask friends, your medical doctor, coworkers (if you dare), other students, and other therapists. It's better than picking one out of the phonebook or off the web, or out of your insurance plan's list. A therapist that other people like is a good recommendation. And say you call a therapist, and they're not taking new patients? Ask them for a list of other therapists they recommend. Likely those will be good ones.
2. Try to figure out what kind of therapy you want. Are you a practical, let's get to the heart of things kind of person? Then Cognitive Behavioral Therapy (CBT) might be for you. Is your life really out of control, with lots of mood swings and instability? Then Dialectical Behavioral Therapy (DBT) might be a good choice. Want the "traditional" kind of therapy? Then Psychodynamic Psychotherapy is for you. Want to spend years in therapy, going over your every thought? Psychoanalysis (the kind of therapy where you lie on the couch) might just be your speed.
3. Money. You've got to be able to pay for it. Some therapists take insurance, but many good therapists don't take insurance and you've got to pay out of pocket. You can often get your insurance company to reimburse you part of the costs if you fill out some claim forms. A good therapist is going to be expensive, ranging from $150 to $400 an hour, depending on where you live. Some therapists will accept a sliding scale payment system, where you pay less if you make less money. It never hurts to ask.
4. Do you like them? You get to the first appointment, and there's something about the therapist you don't like. Go with that feeling. You might give them one more chance, to see if it was a one-time thing, but generally you should like your therapist at the first meeting. Or at the least, feel neutral about them. But if you don't like them, odds are that's not going to go away, and it can make your therapy unpleasant.
5.Tell the truth. Don't be concerned that your problems are too trivial for you to be in therapy, or that your problems are too weird, or that you're a hopeless case. Tell the therapist about the problems you want to work on, and even tell them that you think it's trivial, strange, or hopeless. The therapist has most likely heard it before, or something like it. This way they know what your feelings are about your problems, and can more easily work with you.
6. MSW, MFT, Ph.D, Psy.D, MD? If you need medication, or think you need medication, go to an MD, a psychiatrist. Only psychiatrists can prescribe medication. If you think you just need therapy, a social worker (MSW, LCSW), marriage and family therapist (MFT), or psychologist (PhD, PsyD) would all be good for therapy. Don't worry if you start therapy with one of these therapists, and you decide you need medication--most of them will be able to recommend a psychiatrist or two for you. Again, go with someone you like, and feel like you can work with. If that's an LCSW, fine. The important thing in therapy is the relationship you have with your therapist, not their credentials.
7. That being said, be wary of someone who calls themselves a "therapist," without having any of the above credentials. In some states, anyone can call themselves a therapist, and there's no regulation of them. One so-called "therapist" around here insisted on conducting his therapy sessions in a general's uniform, among other things.
That's all I can think of right now. If I come up with anything else, I'll add it in the comments.