Jazz is radically different from classical music in several ways. Jazz is based on improvisation: Music created and performed spontaneously, whereas classical is structured, "notes-on-the-page". There is considerably more freedom in the performance and composing of jazz music, although it does have its own set of rules. In order to learn to play jazz, the most important thing that you could do is:
1. Know harmony well. Jazz all about understands the intrinsic relationships between different chords. Classic harmony will give you a good introduction.
2. Keep chords sparse, no pedaling, avoid triads in voicing and avoid the root of the chord.
3. A lot about jazz is rhythm and feel. It's very useful to learn to play by ear. Learn to play complicated rhythms by playing it over and over, hearing the rest of the rhythm section (percussion and bass) in your head.
4. Listening to jazz recordings is indispensable in learning to play. Actively listen to the harmony, the sound, the piano solos.
