1. Play the change that is written or is being "played."
a) Written changes - Have a varied vocabulary of ways that you can play common chords and progressions. You shouldnąt be limited by only being able to play your favorite altered dominant voicing, for instance. If the chord is unaltered, you should be able to play a good, idiomatic voicing that is free of alterations. Likewise, you should be able to play voicings that supply either an altered 5th, altered 9th or a combination of the two.
b) Played changes - As an enhancement to a basic dominant 7th chord, a soloist may be playing a melodic idea based on a diminished scale, for example. The accompanist needs to be listening, be able to recognize this unique color and be able to react to it with an appropriate voicing. In this case, a 13b9 chord is implied and that should be the sound reinforced by the voicing.
2. Don't solo while accompanying someone else.
Be careful not to become too melodically or rhythmically active when comping for someone. You may inject a melodic/rhythmic idea that continues or completes the soloist's thought but it shouldn't compete with the solo or distract the listener. Remember, a strong soloist doesn't require any accompaniment at all! So, when in doubt, don't play. Adopt an economical attitude wherein "Less is more!"
3. Surrender yourself to the rhythm section.
A pianist is only one cog in the wheel of the rhythm section. There should be an attempt on the part of everyone in the rhyhm section to establish a "hook-up" or ongoing communication with each other. No one ego should dominate but all should strive for the goal of elevating the music to some higher condition emotionally. When a lead instrument or vocalist is accompanied by piano, bass and drums, it is really a quartet solo. True, one voice is generally prominent and the others supportive but it is primarily a conversation among the members of the group. It is that spontaneous interaction that makes jazz unique and really fun to play!