Choose a piece that you like, preferable not too 'far out', from the jazz 'standards'. Something like 'Autumn Leaves', 'Oh Lady Be Good', 'Satin Doll'... The list is long. Using the chord chart for the song, play along to a recording, playing the root note of each principal chord, on the 'One' beat of the bar. Once that's going smoothly, try slipping in a note on the preceding beat, one semitone lower, so as to climb into the root note from below. Not every beat, but now and again. Try the same thing with a semitone above the target root note, too, and mix 'em up.
If you can get that to work (slowly, at first; a 'slow-down' piece of software could be useful...), then add the beats in between the 'One's, playing notes from the chord. Once this notion 'mastered' for the tune chosen, pick another tune and do the same. After about a dozen or so, you'll start to 'fly'; to be able to hear what's coming up and play whatever you feel is good, not necessarily chord tones. That's when it really starts to become fun.
Hope this helps.