I'm a retired therapist, but as all therapists are individuals, each will have their own way of working with you.
However, (and I hope this helps) for me the first session was always begun by welcoming them, and then inviting the client to firstly ask me all and any questions they had, about therapy options, about me and my experience, and about any concerns they have about confidentiality and any potentially sensitive subjects we might discuss. I would always reassure them that there is no such thing as a silly question, and that they could ask me anything, big or small.
Then once they had asked anything they wanted, I would ask them about what had prompted them to seek therapy. If they are struggling to express this, I may ask them about smaller things first, like what it is that is that they want to get from therapy, for example feeling happier, feeling confident, feeling more at peace, feeling stronger.
Often a client will then talk about the most recent event which has occurred (in as much or as little detail as they feel comfortable with at that time), and in doing so they can also give me indications, hints and clues about whether there are other, historical events which are also involved and where the deeper root of the trauma or crisis may lie.
I do ask gentle questions during a first session, but the aim is not to go right to the painful parts right away because both I and the client need time to make a connection that lets the client feel safe and confident about speaking about their personal life and experiences. I always remember that I will often be the very first person who has ever been told this information, and that is a very sacred trust which I respect at all times. I will often make notes, as this then helps me plan the therapy in future sessions.
I do leave pauses for clients to think about what they want to say, or find the right words. Silence can be a good thing, as it means the client is working internally towards deciding how to express themselves. Please OP, don't think for a moment if you need a pause or silent time to think that it is bad ... it isn't. A good therapist will allow you as much time as you need to find the words you want.
The above process normally takes about 30 to 35 minutes. At the end of it I would, in a first session, perhaps need to ask a few more questions just to double check I have understood and noted all the important points my client wanted to convey. Then I would summarise the potential way forward for the client, such as what type of therapy I believe will help them and what it would involve. I would then ask if they had any other questions or doubts and listen to those and reply as needed.
Finally I would ask if they wanted to proceed with that therapy with me, and then we would agree a schedule going forwards.
That would normally take us to the 50 minute point, which was generally as long as my standard sessions would last.
OP, I have read that you might feel more comfortable with a telephone call rather than zoom. However I would encourage you, if you can, to do the session by zoom as therapists will also get a lot of information from your non verbal signals .. things like your breathing, eye movements, body and hand position etc and a telephone call will not allow them to do these observations. Please don't think you will be judged if you cannot manage a zoom call, but these silent communications can really help a therapist understand how and what you are feeling, so if you can do the zoom call, I would really encourage you to do that.
I hope this has helped, and I wish you every success in your therapy.