I chose to do my three months at place that specializes in "Sexual Minorities", so I went in knowing that they had experience dealing with transgender issues (and my therapist ended up being trans himself). I had previously gone to a couple of other therapists who didn't really know how to help me, or refused to, which was a huge waste of time (and money)--so I wanted to avoid that at all costs.
Overall, it took about four months to get from starting therapy to starting T, some of the extra time was unavoidable, some of it I could have alleviated with better planning. I went to my sessions every other week for three months, because of this schedule I ended up getting my letter a week after the three month mark. For the last of those months I was attempting to get an appointment with a doctor locally, which didn't work out. My first appointment with the doctor that I managed to get, I had my blood drawn for my labs, and I went back a week later (two days ago) and did my first shot.
Regarding the content of the therapy sessions, they pretty much went by the book. I went in completely sure of what I needed to do, and was told on my first session that I was going to get my letter at the end of the three documented months. Most of the time we discussed non-gender related issues, by that point I had been thinking about and rehashing all of my trans qualms with other therapists and in my own head for so long that after talking about it for the first appointment, it became a moot subject.