Dave talks about how he practices … not practicing. It’s the art of improvisation, and it’s key to jazz.
The way to learn improvising by ear is to do it. The way to do it in the privacy of your home is to get the Abersold New Approach to Jazz Improvisation recordings and books. Mix that with listening to recordings and going to see live music, and you’ll be on your way.
If you’re new to playing by sight from lead sheets, here’s a little music theory that will go a long way. There are recurring patterns in the repertoire, and they’re small enough that you can do the same things in any song without interrupting the flow. I’ll mention several for homework and later discussion, then pick a few favorites for detail.
There are many songs that use identical chord progressions. You need to learn 12-bar blues (Abersold covers this), vi-ii-V-I (again, try Abersold), and I Got Rhythm. For long-term planning, the Watters brothers provide advice and a list of songs to know.
Within songs, you’ll often see a diminished chord* followed by a 7b9 a fifth lower: edim – A7b9, Bdim – E7b9, etc. The secret is that all the notes of the fully diminished chord** are in the 7b9, and the rhythm section takes care of the change in emphasis. You can ignore the second chord and by fine. A lot of chord changes are like that: the jazz is in the subtlety, but if you just need to get to the other side without collateral damage, you can simplify.
Another common progression is a minor chord followed by a major chord a half step higher: emin-F, Bmin-C, etc. “A Night In Tunisia” goes back and forth each bar (also see Matthew Herbert’s “The Story”); “So What” goes back and forth at 8-bar intervals. On this pattern you can use tritone substitution–Bb in place of emin, Bmaj in place of F, etc. Bb naturally resolves to F, and B naturally leads to emin (or E). There’s a similar opportunity the other way in 12-bar blues substituting for the IV chord.) The tritone substitution is a jarring, outside sound that should be used sparingly and in context. Also, it’s cool.
With these tools on your belt, you’ll be ready to handle at least a measure or two here and there. A couple of weird chord symbols translates to a small population of notes and a clear idea of what comes next. Improv is music in the moment, and that’ll get you a few good moments.
* there are really only three fully diminished chords, so go ahead and take the time to learn them.
** in the first example, E-G-Bb-Db in edim becomes E-G-Bb-C# in A7b9. See, all they did was add the A.