I generally start by asking around in my social circles, and what I'm looking for is:

1) Usually male, been in practice for at least ten years
2) Experienced with and comfortable working with the issues I bring to the table
3) Intelligence, sharpness, well-read
4) Doesn't use "blank slate" theory; keeps their stuff out of the room, but is still open and human.
5) Willing to talk about the therapy relationship itself with me, a lot and in depth
6) Available to some degree for between-session contact, especially during intense phases
7) Comfortable with queer and poly issues (or a willingness to learn), comfortable with artists and our common quirks
8) Willing to push me, to be blunt with me, to call me on my BS
9) Not too formal

Oh, and the spark of connection that we can like, trust, and work with one another, have compatible personalities.

So - not much. Finding a therapist has sometimes taken a long time and a lot of consults.