Analyze a piano piece before you learn it. Review the scale and main I, IV, and V chords of the key the piece is in; look at the form, or basic structure, of the piece; investigate the main rhythmic patterns of the piece; and look at the chords that make up the harmony of the piece.
Break your piece down into segments of a few measures or a short phrase. For very difficult passages, work on just a few notes at a time.
Practice the right and left hands of a segment separately at first. Often a piano student will attempt to learn a piece by playing through it with both hands. This method may seem faster at first, but it will actually take much longer to learn the piece. You will learn your piece much more smoothly and quickly if you solve the difficulties of each hand separately before putting them together.
Practice your piece segments slowly during the beginning stages. You do not want your fingers to go faster than proper technique allows or faster than your mind can think. Count carefully so that you don't distort the piece's rhythm at this slower pace. When you have grasped the piece at a slow tempo without mistakes in notes or rhythms, gradually speed up the piece to final tempo.
Use your creativity and imagination to create music from the piece after you have put the hands and segments together. You can do this by using different dynamics for different parts of the piece, by observing and shaping the phrases in the piece, and by trying to paint a scene with your piece.
Listen carefully to the sounds that you make. If the sounds coming from the piano are ugly, then try depressing the keys differently. If the piece is supposed to be fluid and soothing but sounds frisky and boisterous, try a more docile approach. However, most piano students don't hear these common faults unless someone points them out. If you can cultivate the skill of hearing yourself, you will become a much better pianist.