For a psycho-therapist that can give you a referral to start hormone treatment, it is on average three months. Many factors are involved, however, like how convincing you are (be sure to be yourself, though) and how trans-friendly your therapist is. Obviously, you need to get one that doesn't hate trans-folk or you're not going anywhere. It also depends on your area. Different places have different policies and ways about doing this.
For me, I started seeing a psychiatrist for troubled youths (ADD, LGBT problems, etc) and it took me about two months for him to really start to understand me. After that point, it was now official that I have GID or Gender Dysphoria (or whatever). The interesting part was that I didn't need to see a psychiatrist at all, as the clinic that I go to in San Francisco doesn't necessarily ask for a therapist's referral. I suppose it was clear as day that I am trans anyway, so I'm sure that helped some. Even without needing a referral to start hormone treatment, my psychiatrist definitely helps me - IMMENSELY so - anyway.