To date, the most effective way of performing on the piano in General and the piano in particular – music. In other words, you must know the musical system before you start to play. This will help you to basic music theory (for example, textbooks vahromeeva or Sposobin).
No matter what textbook you choose: they contained about the same information. The main thing – do them regularly, outline the data. Check yourself, arranging from time to time a kind of tests for memory write rules, the notes in different keys, the characters in the fifths circle, tonality, etc.
Additionally do solfege. One of the most popular musicians of the textbook compiled by Laduhina – "single-voice solfeggio". Play and sing the numbers out there to develop both coordination and hearing voices and artistic expression.
If you have the melody you want to play, the problem is already solved: just play them sitting in front of the instrument. If notes are missing, you will need additional skill – write musical dictations.
Musical dictation a short melodic fragment 1, 2, 3, or 4 voices, performed often on the piano. The student must record it in the notes, without seeing the keyboard, or the original musical text. All he knows - the tone, the size, the number of cycles. Find a collection of monophonic dictation, each play the piano and record the audio as separate files. After some time, play the first of the files and without looking at notes, write down the dictation.
Music colleges and institutes the dictation is played 8-12 times. Try to stay within these limits.
Gain experience and learning to identify melodies by ear, pick up the melody on the keyboard. As soon as possible and play the accompaniment to match the melody with a certain chord grid.