The first lesson has a lot competing for its time. You need to hear the student play, learn a little about them, explain the practical stuff, and teach something worth coming back for.
You won't find out everything. By the end, though, you should have a sensible starting point, and the student should know what to try before you meet again.
Before the first scale
Find out why they came, what they enjoy hearing, and what they would like to play. For a child, invite their own answer as well as the parent's. The answers may differ.
Ask what practice could realistically look like at home. Check access to an instrument and basic materials rather than assuming everything is ready.
If they have played before, invite a familiar piece or pattern. Explain that this helps you choose a starting point. Notice strengths as well as gaps, and avoid making the first meeting a judgment on their previous teacher.
Give them something to take home
A beginner might make a comfortable first sound, echo a short rhythm, or play part of a melody. An experienced student might leave with a more effective way to practice one passage.
Choose something substantial enough to feel useful and small enough to attempt successfully. If your first task proves too difficult, change it. That adjustment also shows the student how you respond when something doesn't work.
Look at the instrument's condition, chair and stand setup, and any immediate access needs. If equipment is interfering, explain the issue and agree on a next step.
Confirm the lesson time, materials, communication method, and payment and cancellation arrangements. Supply written policies so a brief conversation does not have to carry every detail.
Save the last few minutes
Ask the student to show what they will try at home. Give a short assignment with a starting point and a clear focus. For a child, involve the parent in the way that fits the family's arrangement.
“Try the first four notes slowly and listen for an even sound” gives a beginner more direction than “practice what we did.” Adapt the task to what they can actually do without you.
Fitting it into half an hour
In a thirty-minute lesson, you might use a few minutes for conversation, a short period for assessment or a first demonstration, most of the remaining time for one musical task, and the final minutes for the recap and questions.
Those are proportions to adjust, not a checklist to finish at the student's expense. A student needing more time to become comfortable may need a different balance.
Finish by naming one thing you learned about the student and one thing they can work on. Clear practice directions help that first meeting carry into the week.