In my case, my health records were reviewed with the doctor's assistant that day before seeing the endocrinologist herself. We went over my medical history, medications, etc. A brief, non-invasive examination also took place (blood pressure, abdominal palpation, heart & lungs). Then I met my endo and she very respectfully asked a few questions about where I was mind-wise with the whole thing. She wanted to know what name and pronouns I was going by and how I was being regarded by others. We reviewed my most recent blood work and she confirmed that everything looked good. Then she explained what options were available and which options are covered by insurance. We talked about the desired effects and also the potential side effects of T. She wrote me a prescription for a low dose of T which I could start ASAP and said we would gradually increase the dosage, meanwhile monitoring the progress via my GP until I would see her again in a few months. She was also happy to answer any questions I had. It all went very smoothly and there was no screwing around. I was treated with the utmost respect and kindness and didn't have to endure an interrogation or any such nonsense.
EDIT: I forgot to mention that she also asked what kind of support I have and if I was involved in any trans groups. Then she recommended some local support groups and information resources. She also highly recommended that I continue seeing my psychotherapist through the transition and to report any problems.