Gary Burton, jazz musician extraordinaire and master teacher, is giving a free course online through Coursera. I've taken it.
Gary's first point: Improvisation is a language with a vocabulary of sound. This consists of chords, scales, and licks. It requires an ability to hear these internally and then assemble them in real time. And finally, there is your ability to develop a story, with sound, on the fly.
Gary's second point: Sounding like a jazz musician through memorizing licks is like memorizing French phrases and heading to Paris. You may sound French; however, things quickly break down when you are spoken to.
2023 update. It was an interesting course; however, it requires a high degree of keyboard skill to get the most from it. Below are some exercises for beginners who have intermediate skills which involve broken chords, a bebop lick, and a chromatic approach. It was inspired by a Chase Sanborn story, who discovered his jazz solos improved when he left notes out.
Creating Jazz Solo Lines
You've got to learn your instrument. Then, you practice, practice, practice. And then, when you finally get up there on the bandstand, forget all that and just wail.
I'm a professional pianist and music educator in West Toronto Ontario. I'm also a devoted percussionist and drum teacher.