Sit at the piano with the student. This will allow you to play music and observe as the student attempts to reproduce what you played.
Play the full piece for the student. If the student is familiar with the way the piece is supposed to sound, she will be able to more easily reproduce it on her own.
Divide the piece into sections, and review each section with the student. Learning an entire piece is easier if the student learns one small part at a time. Have the student play the first section and move from one section to the next until he has played the entire piece. Return to difficult sections and repeat them until he can play them well.
Have the student visualize the fingering on the keyboard as it is played. Many students who play by ear also memorize chord shapes and note runs as they appear on the keyboard.
Have the student hum, whistle or sing along with the melody of the song. Many students who play by ear can learn better if they can reproduce the piano music with their own voice. This can help cement the sound of the piece in the student's mind so she can reproduce it later on piano.
Record the entire piece with an MP3 recorder so the student can play along with the piece at home. You may also record individual sections so the student can work on the sections that he may have difficulty with. The recording is a good home substitute for playing with you in person and will prepare the student for his next lesson.
Focus on developing the student's muscle memory. Muscle memory, or the body's subconscious ability to remember fine motor movements and sensations, is essential to playing any instrument but particularly for students without the crutch of sheet music to tell them what to play. Repetition helps develop muscle memory, so students who play by ear can benefit from relaxed, precise repetition of musical pieces. The goal is to develop muscle memory so fully that the student can play the music with a relaxed focus and her body will know what to do.