Most first sessions with therapists (I've had four, and this has been my experience with all of them) go a little something like "here is a questionnaire I want you to fill out. It's sort of a gauge of your current mental health and what you want out of our time together". They usually ask you to come early that first appointment so the questions don't cut too much into your therapy time. They'll go over the sheet with you and make sure they understand your answers, ask you to elaborate on some, and make sure what you want is something they feel they can help you attain.
With gender therapy specifically, your therapist will probably ask you how long you've had the dysphoria for, what kind of dysphoria you've experienced, what made you question your gender, and any major events in your life related to your gender feelings. They will also ask questions about what kind off support system you have, if and where you are out, whether your family is aware, and what your transition goals are. They may also ask about your sexual history. I'm not quite sure what the purpose of that one is other than perhaps antiquated notions of "trans people are actually just homosexuals" or perhaps to gauge whether past abuse may factor into the matter.
It will be emotionally draining, and it is scary, but making the appointment and showing up is usually the hard part. Once you're there, you'll probably start talking. I'm fairly reticent IRL, and I babbled for about a half hour straight about my life when I went to my first gender therapy appointment.
It's mostly about whether you want to be there or not and how comfortable you are with the therapist. If you don't click, find someone else. The first try isn't always the right person for you.
