One of the best ways to learn improvisation techniques is to transcribe solos by iconic artists and analyze their ideas. Of course, nothing will teach you more about improvisation than real improvisation. There are three methods of improvisation in jazz: melodic, harmonic and motivic. Improvised melody occurs when musicians use insults, alternate notes, and syncopations to recreate the melody in new and interesting ways.
Harmonic improvisation uses chords and centers of tones to inspire new solos. Improvising by redefining motives, phrases and statements serves to sophisticate the musical arrangement. Just as no two artists would paint a scene in the same way, no two musicians improvise in the same way. Experienced jazz musicians combine all three techniques to create new works, drawing inspiration from the original melody, harmony and structure that represent their unique creative passion.
The true value of this music lies in the individual creativity of each artist and in that unique process of expression that is jazz. If there's one thing about playing jazz that's shrouded in mystery, it's improvisation. Improvisation exists in other types of music, even in musical traditions from the far corners of the world, but in jazz it goes much deeper. In some ways, it's vitally linked to the spirit of music, and it's not just musicians who recognize the power of improvised solo.
This essence has been reflected in everything from literature to movies and pop culture.