I've never felt anxious going to therapy but I don't think the anxiety is particularly abnormal either. My first time seeing one was around 20 years ago so maybe I was more anxious than I remember
I've only seen therapists for my talk therapy. We just...talk. They usually let me take the lead. I discuss things that have happened since I saw them last, what is worrying me, etc. IME the therapists are just good at listening and asking the right questions to help me figure out what I need to do.
I'm biased but I think everyone can find therapy useful.