A "fake book" contains songs written in a concise format that includes only the melody and chords, letting you interpret the song's performance according to your own taste.
The songs in a fake book have a single melody written out in notes with the lyrics written beneath the notes. Above the notes of the melody you'll find the names of the chords to play.
This format is very compact. You will often see fakebooks containing 500 or more songs. Here are some suggestions on how to use one of these songs for increasing your improvisational skills:
1. Chords. The suggested chords are often very rudimentary. Most jazz pianists spice up the songs with more elaborate chord progressions. Try to find more chords to use in the song. This exercise will increase your skills in chord theory.
2. Scales. When you have elaborated upon the chord progressions in the song you can choose scales that work with the chords you have chosen. If you find this hard to do you can buy scale books with scale suggestions for different chord progressions. This is an exercise in scale theory.
3. Practising piano chords. Start with the first chord in the song, play it in different positions on your piano and in different combinations.
4. Practicing chord progressions on the piano. Take a couple of bars of the song and practise to play the progressions over and over again varying the chord voicings.
5. Practicing scales on the piano. Begin with the first chord and the scale you have chosen with it and start by playing the scale up and down the keyboard with the right hand and the left hand.
6. Practice piano improvisation with scales. As soon as you master playing the scale up and down the piano it is time to create music with the scale by playing around with it, creating patterns and inventing melodies.
7. Practise piano improvisation. Take a couple of bars and play them over and over again with chord voicings in the left hand and improvising with the appropriate scales with the right hand.
It is also good to practice piano improvisation with your left hand and voicings with your right hand.
There are of course many more things you can do with a song in order to develop your skills in piano improvisation. Help yourself and don't forget to have fun and to also play the song in its entirety with the melody.
