It opens on the last graded thing
A good first session starts with the most recent test or homework that came back marked. Not a syllabus, and not a placement test the tutor wrote — the paper the school already graded is the only evidence in the room that nobody has an interest in.
Listen for questions, not explaining
A tutor who spends twenty-five of thirty minutes explaining has not found out anything. The half hour is a diagnosis, and a diagnosis is made of questions. You can hear the difference through a door.
Two questions worth asking out loud
Ask what they think the actual problem is, and ask what the first four weeks would look like. Both answers should be specific enough that they could turn out to be wrong. *We will build confidence* is not one of those answers.
What it is not
It is not a lesson and it is not a sales call. Nobody should come out of a first half hour holding a package to buy — on this site the first thirty minutes are free and nothing is sold inside them.