I researched types of therapies and types of therapists. I had an idea of what I wanted anyway. From there, because I wanted someone psychoanalytically oriented, I contacted the nearest psychoanalytic training institute for a referral to a candidate (student). Candidates are carefully screened, and are experienced therapists.
I received one referral to try and that is my T. The location was right and I liked her when I met her, even though I was certainly intimidated too.
She meets with prospective patients a few times to see if she thinks she and the patient can work together. After a few visits, I asked what she thought. lol. She had already decided we could work well together. I thought so too. I was nervous and angry when I left the first visit about some minor thing, and at the 2nd visit she was soooo gentle when she asked about it, and so accepting and non-judgmental and I knew that this was the person I wanted to work with. It still took a long time for trust to build, but that was a good indicator to me that she was trustworthy. Over time, she was reliable and didn't cancel sessions, she made time for me when I needed an extra session, once even coming in on her day off. She is kind and accepting and patient (although I had to get through a long period of time where I thought between sessions that she was anything but those things; my fears were at work, distorting my perceptions).

I've had other T's and they were okay. Only one who wasn't a good fit because she didn't tell me that her orientation is hypnotherapy and that wasn't what I was looking for. She also cancelled my standing Friday appointment every week for a month and wasn't concerned until she realized I had stopped rescheduling...