So I'd like to know how to play some jazz on the piano. The only thing I know is that I've heard from my friend that when you play a chord, you don't play the root. I tried it and it doesn't seems right, maybe there's more to it.

On a tangent, there's a song that I'm trying to play, and it doesn't give chords. I'm trying to make it a Sax piece with piano accompaniment. The left is given chords. The right hand had has the melody and that's given to the saxophone. What should I do for the right hand?

You should listen to stuff. There's plenty on youtube (http://www.youtube.com/watch?v=mFNkAp-FmSs).

If it's only sax and piano, you should definitely play the root. Pianists don't "have" to play the root when the bass is there, since the bass plays the root.

If you have a lead sheet (which is just melody and chord symbols, not chords written out note-by-note)..well..the point is to improvise. Use the chord changes as a starting point and build of that. It's not going to be easy to try and play good jazz when you're just starting out. If you really want to you could find a written solo and just learn that...but then it's no different than classical music.

"On Classical Piano, there are two wrong notes each to every right note. On Jazz Piano, there are two right notes each to every wrong note." --Anonymous

There's a quote that I generally live by when I'm playing in the jazz style; anything goes when you're playing jazz, since jazz is more of an 'emotionalist' art and a fine art, one could say... at least in my honest opinion.

I'm sure somebody asked about this, maybe, a year or two ago, and the advice I gave was very structured and filled with rules. I've become much less of such things as time has passed. Sure, there are "jazzy" scales and the theory of "blue notes" that are characteristic (I suggest you look those up...blues scales...bebop scales...there's a LOAD of scales out there to use in your improvisational and stylistic arsenal) of jazz.

Just remember this, "Have fun." That's the point to music, and the heart and soul of jazz. It's about just going with where your heart tells you to go.

Oh, it's fun to play crazy scales, but you don't always have to be Charlie Parker playing hard bop. ;)

EDIT-- And as far as "not playing the root." That's part of an un-written part-writing rule for jazz in a big band...I tend to play the roots on some chords and no on others-- just what sounds jazzyist :P