How to improvise? Make up a melody and play it on your instrument. Keep doing that until you're thinking musical lines and can find them on the instrument quickly. Want to improvise with others? Learn chord progressions. (Harmonic line). Then learn the scales and arpeggios that go with each chord. Want to learn harmonic lines? Transpose each chord progression into every key. Want to get better at it? Study all the music you can in the style in which you want to improvise. Want to be a great ensemble musician? 1. Play the right notes at the right time. 2. Make everyone else sound good.

Sounds simpler than it is.

Frank Hamilton