Start by imitating your favorite players. Copy their licks and transcribe their solos from recordings. Also attempt to emulate their sound and the subtle inflections that create the magic in their playing.
Here’s what Clark Terry has to say about the first step:
By imitating the players you love, you’ll begin to understand the music on a deeper level and begin to see a personal sound develop in your own approach to improvisation. Questions that can’t be answered by music theory or etude books, like how to play longer lines or how to articulate and swing, will reveal themselves as you start to imitate the masters.
Then go on to assimilate, or integrate, what you’ve been imitating. Allow your models phrasing and ornamentation to become a part of your own style.
Again from Terry Clark:
Assimilation means ingraining these stylistic nuances, harmonic devices, and lines that you’ve transcribed into your musical conception. Not just mentally understanding them on the surface level, but truly connecting them to your ear and body. This is where the hours of dedication and work come in.
Remember the licks and patterns are like words and sentences. In and of themselves they are not improvisation. A key element is to practice and integrate the phrases, scales, and patterns into actual playing and in context with the music.
Practice your licks and scales with Play-Along tracks to work out how they sound in context with music. Even better play with real human beings. Through trial and error develop you’ll the confidence you need to fully truly yourself.
Innovate what you’ve learned and make your own. Little by little change the licks. Experiment and try different things. Combine elements, after them and make something new.
On to the third step from Clark Terry, innovation:
Creating a fresh and personal approach to the music. Many young musicians want to skip to this step as soon as they start learning how to improvise… Innovation is the direct result of hours upon hours of imitation and assimilation. Take a look at the great innovators that this music has already seen. Each one spent countless hours studying harmony, solos, form, tunes, etc. in order to realize their own personal concept.
This three-step system is all based on the presupposition that you listen first and during all three stages.
Listen to recordings from great players.
Listen to your teachers and fellow musicians.
Listen to what coming out of your instrument.
And finally, but most importantly, listen to that small voice inside yourself that is the fountain of all beauty and music were creating.
This is what guides your decisions and connects you to your inspiration.