Listen to Johann Sebastian Bach's "Two and Three Part Inventions" and his "The Well-Tempered Clavier." This music provides the very definition of theme and variation. Each piece begins with a theme, then continues with one or more variations on the theme, followed by a recapitulation of the original theme and a conclusion. This musical paraphrasing shows a variation can also be a comment on the main theme.
Listen to Django Reinhardt and Stefan Grappelli's "Le Quintette du Hot Club de France." Although the quintet doesn't have a saxophone, Reinhardt and Grappelli are talented jazz stylists and improvisers, with Grappelli improvising off of the melody on his violin while Reinhardt's muscular arpeggiated runs illustrate the power of chord-based improvisation on the guitar.
Listen to the music of the great bebop saxophonists Charlie "Bird" Parker and John Coltrane. Start with their renditions of popular songs such as Coltrane's "My Favorite Things," with its establishment of the vocal theme followed by long, improvisational solos. You could also start with Parker's "Summertime," where his tenor sax follows the vocal melody, but does not copy it note for note. Sing along with his sax and see what happens. Listen to different renditions of the jazz standards; compare "Night and Day" as rendered by Django Reinhardt and the Quintette, the Charlie Parker Quartet and Oscar Peterson's trio. Never stop listening.
Find a music teacher and learn the basics of your instrument. Study music theory with dedication. Go beyond the circle of fifths and triads and scales; learn the modes that are built on top of the major scales with their big, extended chords. Modes are the building blocks of much improvisational jazz music.
Find local jazz enthusiasts and play with them. Get to know each other well through your music. Add a little life to your music by channeling your emotions through your playing. When your heart is broken, hit your sax and play your way out of it.