Get to know the different rhythms of a jazz piano. Each jazz style (Swing, Bebop, etc.) is dependent on beat and has a unique rhythm. Play different rhythms in the bass line. A walking bass, for example, is played with the left hand in the lower keys of the piano by playing quarter notes within a chord or scale. For an A chord, you could play A, C sharp, E, C sharp (chord tones).
Emphasize weak beats, also known as syncopating. Usually in music, the first and third beats are strongest. In jazz music, the second and fourth are emphasized by resting (or not playing a note) on the normally strong beats.
To create a stronger syncopation, rest on only the first half of the first and third beats (by using a eight rest and eight note).
Swing eight notes. One of the key elements in the jazz feel is the swing rhythm, accomplished by playing uneven eight notes. In a pair of eight notes, play the first note longer than the second to create an uneven, broken pattern. Do not hold all the notes for the same amount of time.
Practice jazz/blues chord progressions. A simple and common progression is the twelve bar blues (a bar is a measure in music), which includes progressions among the I, IV, and V chords. In the key of C, the chords would be C (I), F (IV), and G (V). Start on the C, and move between the C and F for various bars, adding a G chord, until you have a pattern with twelve bars.
Improvise over left hand patterns. After establishing chords and rhythm, improvise with the right hand in the melody by using notes from a chord or scale. Remember to employ swung eights to offer a better, jazzier feel.
Add more depth and complexity to the basic music. Throw an extra minor II chord in with the basic chord progression. Employ seventh and ninth chords into a song. Use jazz modal patterns to create more decorative improvisations, and employ the blues scale to add a grittier feel.