Listen to as much jazz as you can. I'd start with things like Count Basie, Duke Ellington, Louis Armstrong, Charlie Parker, Miles Davis, Dexter Gordon, Jazz Messengers, Horace Silver. A lot of key stuff there. Swing and Bebop. Real "meat and potatoes" jazz. Maybe some Stan Getz.
If you have access to any of the Jamey Aebersold stuff, try playing along with some of the basic ones like Major/Minor, Vol 1, ii/V/I, Vol. 15 Payin' Dues, Vol 54 Maiden Voyage. You could start playing by ear, not to many notes, just really trying to fit in and sound good.
But, I'd really listen a lot to Parker, Miles, Jazz Messengers/Silver. It's all in there.
Besides the good info in the books with those play alongs (Jamey's scale syllabus is helpful, but use your ears and don't be afraid of adding in chromatic notes), you could definitely try a few of the basic solos in the Omnibook and work at playing them in the bebop style. But, spend some time just playing along with the backing tracks, CDs, whatever just using your ears. No music.
If your trying to learn a tune, try playing choruses of just working the bass lines, then some apreggios, then resolving guide tones (e.g. 7th of chord into the 3rd of the next chord). Play the melody multiple choruses, and loosen up and play it in different ways. Mix it up, but stay close enough to be recognizable. These are always good exercises.