When playing stuff like Vanessa Carlton music, play with your wrists, not your fingers. Put the right fingers down further than the rest of them and roll your wrist.
Obviously, this doesn't apply to all piano music.
Also, assuming you have a decently maintained and good quality piano, you are going to want to be ligher on the lower octives and harder on the upper octives. If you have a cheap piano, this won't do much of anything.
When comping a band on acoustic piano, try to stay above middle C. Your sound will get lost the lower you go, because lower frequencies blend right in. The higher you go, the more you will be heard. But, you want to avoid being in the same range as a soloist, so be careful. As a general rule, never play in a higher range than the soloist.
Learn where your piano sounds good. Unless you have a shweet Steinway 9' Model D, this will be a problem. The first and second octives are "muddy" most of the time. They will give you really bad sound. Avoid them, even if your part notates stuff down there. Transpose it up a few octives. Also, avoid the upper two octives. Generally, they sound "chalky."
Don't get addicted to the sustain pedal. If you rely on it too much, you will find yourself screwed over on something like organ or a synth without a pedal. Use it when you need the effect, or when you can't reach notes otherwise. Otherwise, leave it alone.
Uh.... I guess that is about it.
