I will lay out here a simple program which if followed exactly will have you improvising like the greats in a very short time!
1) Take a solo of one of your favorite players on any instrument. Learn the solo exactly (spend time on this, even if it takes you weeks.) Spend a little time each day moving ahead a bar at a time. Do it in short spans of time, say 10-15 minutes and then totally withdraw from it the rest of the day, but do this daily. Continue until you have the whole solo down (write it out if you are able to).
2) Now analyze the tune in its entirety. Learn every chord change and really do a thorough study of the logic of the progression and the melody. Learn the lyrics if it has any. Work out all the scales involved with the chords and completely analyze the solo you just learned against this data.
3) Now comes the fun part. With what you've learned from having done (1) and (2) above, start soloing on the tune. Use a metronome and start at a slow tempo and really say something. Gradually increase the tempo until you can fluidly improvise and play a solo that makes sense. Don't rush this step, continue to the point you feel totally confident soloing on the tune.
4) Next, tape yourself soloing on the tune. Listen to it and critique your solo and work on any weak points and then tape again. Do this over and over till you are confident in your ability to solo on the tune and this is backed up in your estimation by the tape.
5) Now for the finishing school part of this discourse: Having made a tape that you feel is competent, take the original solo by your favorite player that you learned. Listen back and forth to your solo and his/hers and compare the two solos for quality, not for carbon copying, etc, but for cohesiveness, content, excitement level, compositional structure, etc. Practice soloing on the tune with what you've learned from the comparing and when you are ready, re-tape another solo and compare it to your chosen original soloist. You could have a second musician whom you feel is competent listen and compare the two solos but it isn't really necessary. Do this until in your eyes, your solo is as good as the master's solo.
The final product -- A greatly increased ability to improvise. Try it again with a solo of a completely different genre. You soon will be a master yourself.
I'm very interested in your progress with this program. Feel free to email me with any questions or successes.