I only wanted psychodynamic-type therapy, so I called up one of the institutes for psychoanalytic therapy in the area. I spoke to the intake worker over the phone and she asked what my specifications were, if any. I said, "Just make sure the therapist is male." A couple days later, my T contact me and we set up a session. So it was basically random. I did not pick him and I knew absolutely nothing about him. He was essentially assigned to me and here we are, four years later, and I don't think I could have found a better match if I had researched every therapist in my area.
My therapist ended up changing agencies, but I went along with him.