A quick way to learn how to play piano (and guitar!) is to hone in on how to play Chords in the context of some simple Chord Progressions. If we vary how we play each Chord within those Progressions, then we can even move straight into some simple Improviation. This can be very fun and motivating!
Gary Rosato's "Let's Enjoy Piano Self-Expression Method" follows a similar pattern. This video is a very good example.
Another person by the name of Chris Russell Robinson gives an excellent demonstration of this type of thinking too:
Be sure to read the video description:
[...] These are techniques I use to learn a song by ear (or when I just have the fake chords to go by). It is quite basic, but I think it is a good place to start if someone is trying to bump up their piano style. [...]
This assumes you know how to read fake chords (Cmaj7, Am7, Gsus7) and voice them at the piano without sheet music.
1. Practice voicing the chords for the song and move through the progression with the most efficiency. The fewer the note changes the better. If you have to pick up your hand too much and move it around between chord changes, stack your chord voicings closer and tighter.
2. Once you have your voicing placed, progress through the changes with both hands. Knowing the chords in the right hand lets you practice stride or walking bass with the left. Knowing the chords in your left hand lets you practice the melody in the right. Eventually you can switch back and forth during a song and people will think you are amazing.
3. When you have the chords solid in both hands, start bouncing and syncopating the rhythm between the two hands. Move both hands on top of the chords like you are playing bongos.
4. Arpeggiate the chords in the right hand, jump around the chord tones, and leave out notes here and there to start a very rudimentary improv solo. Once you have that down, try playing the melody with your right hand and use those chord tones to fill in around the melody. You can connect the chord tones using chromatic scales, blues scale, major, minor, whatever, once you are comfortable. What ever you play as the melody, use the rest of your right hand to fill in chord tones below it. And you don't always need to use all the chord tones. The root and the fifth can almost always be skipped in your harmonies.
5. Once those chord tones are anchored in both your hands, most your improv will come from just those notes. You can always make your chord tones more complicated to spice things up (A G9+ instead of a G7, for example). A melodic jazz solo never has wrong notes. If you accidentally hit a note that you didn't intend for, roll chromatically up or down until you land on a chord tone and you are home safe. People will hear your recovery and think you meant it because you are a genius.
Once these basic ideas are mastered, not only can we play a lot of Songs and Improvise, but we can more easily learn to play Scales in the right-hand over Chords in the left-hand! This skill can lead us to more sophisticated types of Improv.