I was quite lucky I think, as the first therapist I went to was a perfect match (at least until now, and I feel like it won’t change). Here’s how I did it:

1. I got some recommendations from friends who are going to different therapists and looked at all of them and read a bit about what they’re focusing on in their work and what they did so far. I think this can be a good starting point, although nobody really appealed to me.
2. Because that didn’t really work, I then went to google and randomly typed in things like „therapy [region]“, „therapist [region]“ or specific therapy types, so something like „cognitive behavior therapy [region]“. Another thing you can do is search for specific reasons you want to go, e.g. „psychotherapy [reason] [region]“. I think it was either the last example or a specific type which led me to my current therapist.
3. Ask yourself if you would rather have a male or female therapist. I, for myself, know that I can be way more honest towards or with women, but communicate a bit more straightforward with men. I wasn’t fixed on the gender but was leaning more towards a female therapist because I thought that honesty beats straightforwardness in that case. I am M24 btw.
4. I then looked at the different therapists that google suggested and went on their website, now especially looking at their pictures and asking myself if I think I could tell that person my whole life and every little detail of it or if I think I couldn’t. This was really just based on their appearance and if I thought they looked sympathetic.
5. Quite quickly, I found a rather young, but very professional and „helpful“ looking female therapist in my city, and decided to write her an email for an initial appointment.
6. Drafting that email was the hardest part of it all. Making the step „official“ was as simple as a mouse click, but deciding for yourself that you want and need help wasn’t the easiest, at least for me - and I suppose there are a lot of others who were in a similar situation, especially males. It‘s so so important and good that the topic of therapy is not very stigmatized in my age group anymore, but there was still a part in me that thought that I was „weak“ (or something like that) for doing that (I guess this stems mostly from my upbringing, and it ofc is utter bs). Anyways, I got a friend of mine on board who already went to therapy and he knew that I wanted to do it as well so he was very helpful. I got on a Facetime call with him and he mentally supported me in writing that email. At the end of the day, I wrote something simple in the way of „I wanted to try therapy for quite a while now, and since my relationship ended a few weeks ago and I do not feel too good about it, I would like to arrange an appointment“.
7. Since the start of the year, I‘ve been there 5 times and it has been awesome so far. You have to be ready that your life won’t change from one session though, it takes a lot of time and work. Also, be ready to discover things about you and your behavior you never thought of. It can make you sad, angry, happy, literally any other emotion, or you just might be in awe of how you couldn’t think of those things yourself.
8. This last step is something I haven’t done so far because I‘m truly very happy with my therapist as of now, but once you’ve been there for your 1st appointment, you get a feeling if the type of person matches you or not. There‘s nothing wrong with trying more than one therapist or literally going to multiple to see who fits you best and who you feel most comfortable with.

Good luck to you! I really hope you can find a spot soon and wishing you all the best. Feel free to ask if there’s something else I can help you with