Jazz improvisation frustrates learners because it looks spontaneous but rests on deep preparation. You cannot freely improvise over chord changes you do not understand, using a vocabulary you have never practiced. The magic is downstream of a lot of study.
The path moves from theory to vocabulary to the real masters. First understand the harmony, then build a stock of usable patterns, then absorb the language directly from transcribed solos.
Learn the theory and the scales
Start with the field's standard reference. The jazz theory book by Mark Levine explains chords, scales, and how jazz harmony actually works, and it is the book most players return to for years. Pair it with Scales for Jazz Improvisation, which drills the chord-scale relationships until they are under your fingers.
Build vocabulary and bebop language
Theory tells you what fits; vocabulary tells you what to play. Patterns for Jazz is a huge catalog of melodic patterns to practice through all keys, and How to Play Bebop, Vol. 1 teaches the specific language of bebop lines that underlies modern jazz.
Practicing effectively matters as much as what you practice. The Jazz Musician's Guide to Creative Practicing and Improvisation for the Contemporary Saxophonist, both by David Liebman, are unusually honest about how to structure the work so it compounds. If you play piano, The jazz piano book is Levine's indispensable companion.
Connect the lines and study the masters
To make lines flow across changes, Connecting Chords with Linear Harmony is a focused, practical book on voice-leading through progressions. Then go to the source: Miles Davis Omnibook and John Coltrane - Omnibook collect transcribed solos so you can learn the language the way every great player did — by absorbing it directly.
Books and transcriptions point the way; playing with others and listening constantly are what turn study into music. Follow the full path in order.