Oh, I wanted to post earlier, but then got sidetracked.
I've been in therapy several times. Firstly, I don't like going to an initial consultation "cold." I like to call a therapist and ask them about their approach and how they work before scheduling anything. If they don't want to take five or ten minutes on the phone with me to give me an idea what they are about, or to ask a little about me, I won't make an appointment.
Once there, I need to feel that how I express myself is understood by the therapist. If they consistently misconstrue my words, give advice that doesn't make sense to me, and need me to reiterate what I said over and over in different ways before they get it (this has happened!), we obviously have incompatible ways of communicating. I don't mind explaining what I mean once in a while, but I want someone who gets me without my having to explain myself again and again and again. Not just because it's frustrating, but because I am paying for that time, and that time and money are wasted if I am spending a lot of it rephrasing what is bothering me.
Right now I am not in therapy, but am working with a personal organizer who comes into my home (a vulnerable position for me!) and helps me with my clutter and chronic disorganization, and she gets what I am about immediately - so the hours we spend together are very productive.
I think another thing that is important is empathy and compassion, and a therapist who makes good suggestions on how to handle or deal with whatever issues you have going on. I have worked with a therapist who was very analytically-oriented, and some that are all about re-examining my past and shitty childhood, etc., and that is fine (they need some background info, after all), but I like the aspect of having a place to fall apart a little in the here and now, where it isn't all about fixing me or analyzing me, but letting me have an outlet, where I am treated gently if I need it. However, I can be a bit self-indulgent in that way, so they also have to have good sense of boundaries and know when to say the thing that will snap me out of it. If they let me vent but will not let me wallow and then give me "assignments" so I am accountable to them, or help me find ways to create new options or perspectives for myself, it seems to work best.
You are only going to get a sense of these types of things after a few sessions, I think. If you don't find a therapist that you click with, you may want to look into a life coach where the focus is more about setting goals and accomplishing them, rather than digging up the past and analyzing things to death.