Obviously every piano teacher is different and therefore every piano teacher can teach slightly differently but in the very first lesson, there are a few basic things that need to be covered and it is probably common to most, if not all piano teachers.
The first thing I start with is how to sit and the piano. I cover how to work out how far you should sit back from the piano and why. I also cover how you should position your hands and fingers over the keyboard. This is important as it keeps you in the most comfortable position while playing the piano, whilst also help avoid any muscle strain or stiffness. Most piano teachers, if not all, would include this in the very first lesson.
The next thing that I usually cover is the names of the notes. This might seem a lot, but I only talk about the white notes and what they are called – which is the first 7 letters of the alphabet. So the names of the notes are quite easy to remember. I also explain that they are repeated multiple times on the piano keyboard and what the pattern is. A lot of teachers do this, although it is not always in the first lesson, but it is typically covered in one of the first few lessons. When I am teaching, I will always make sure that the student has an understanding of what I am teaching before moving on. You will find that any piano teacher will make sure that the student understands this before covering something else.
What is next for me when I teach, is teaching just three notes in the right hand. Once a student feels confident to practice those during the coming week, I move on to teaching three notes in the left hand. I do this because my absolute favorite piano course that I use, is designed this way and over the decades that I have taught, I find it to be a very good way to get a student started.
You would find that by the end of the first lesson , your piano teacher would have taught you a few notes to play and they would have set you what you needed to practice for the coming week.
It can vary quite considerably when a piano teacher will introduce how to read those few notes from the music notation. Often this will be included when I give a student their very first lesson, but if they are feeling overwhelmed, I introduce the notation in the second lesson.
I am confident in saying that for most piano teachers, this is the typical content of the first lesson. What you would find is that the explanations and presentation of the information can vary dramatically between teachers.
I know for me that the first piano lesson I teach for someone, most of the lesson is taken up with me explaining things. From the second lesson onwards, there is much more time with the student playing and I spend only a fraction of the time talking.
I think it is important to state that in my opinion the first piano lesson is the hardest lesson you will ever have. In the first lesson, there is so much information that is taught, that it can be overwhelming at times, but piano teachers are very good at helping a student to work through the material so they are no longer overwhelmed. If you can get through your first piano lesson, you can successfully learn to play the piano.