In a typical piano lesson plan you will begin by warming up your fingers with scales, arpeggios, broken chords and other exercises that will promote strength and flexibility in your hands.
Once you’re warmed up, you will practise pieces from the classical or contemporary repertoires. It is entirely up to you which style you would like to follow, although I usually offer some basic training first so that you can read music from score and learn how to play a few simple pieces.
I strongly believe that good musicians combine reading music from score as well as playing by ear. For that reason I tend to record practice pieces for my students. Listening to them before practicing at home helps to develop listening skills, being better at the rhythm and remembering the melody after the lesson finishes.