How does an engaged person find a chosson/kallah (pre-marriage) class teacher? Preferably a good one?
Is it "just ask around"? Ask a rabbi? Is there any good way to compare different people, or is there just "the usual person"?
Probably depends on the community and on the chassan/kallah's personal situation. But in many cases, "just ask around" is indeed the best approach - they should talk to their friends who have recently gone to such classes.
That's what I did before my own wedding. I got the names of a couple of good chassan teachers in my neighborhood, but I was also advised that the best one is Rabbi S.B. Chaikin, in Cleveland; so I went there.
I lived in CT when I was engaged and there are apparently not very many Chosson teachers in CT. There was one rabbi who I asked to be my Chossen teacher and he told me that he would not do it and not every rabbi can necessarily teach these topics as it is one thing to do this in practice, but a whole different thing to teach to a Chossen. I asked at the Bridgeport Yeshiva and they recommended a rabbi in Monsey (about 2 hours away for me). I met with him in Monsey a few times and otherwise learned with him over the phone and I think he did a very good job.
It's important that the rabbi does not just teach the Halachos of Taharas HaMishpacha, but also everything else that is part of being married.
Might be worth trying yoatzot.org; I think they offer some teacher training so they might be able to recommend teachers. (While primarily for women, I wouldn't be surprised if they knew of male teachers too.)
I think Young Israel occasionally runs teacher training for its rebbetzins, but again, I'm not sure how many such teachers they are or where, or who to contact.
My impression is that depending on the size of the community and role the the rabbi/rebbetzin, sometimes they're the ones giving the classes, but in a larger community, or if the bride/groom doesn't currently have a clearly-defined synagogue rabbi, it becomes "somebody else's problem."
The OU says they're working on talking with rabbis and schools about improving pre-marital education, so we'll see if this changes soon.