I don't know about specialized treatment for sexual addiction, but can answer your questions for general therapy.
Around New York City, I think 175 per hour is typical. Figure it is somewhat cheaper in most other places. Insurance usually pays for part, typically half. Once a week is a typical frequency but the therapist will have advice on this.
How does it work? Therapists like to say that the process is "directed conversation in the service of change". In practice, the counselor is like a friend who is a good listener but with some key differences. First, the counselor has a lot more experience dealing with problems. I mean, all day long they deal with troubled marriages, difficult kids, addiction issues, etc. and they learn from all this experience. You get good advice. Second, they are not trying to please you, to say what you want to hear, like friends do. A good book to read is "Too Soon Old, Too Late Smart: Thirty Things You Need to Know Now" by Gordon Livingston.
Good therapists focus on actions -- what steps can you take now to move down the road to where you want to go.
The counselor I see is like a personal coach. He is a tough-as-nails Irish guy originally from staten island. Very practical advice (. . . tells me to focus on my business now, and deal with relationship issues later, just keep the peace.)
Anyhow it can be great. Take the time to find someone you like. Hope this helps.