Breathe properly and maintain proper posture when playing. Wind instruments require you to breathe from the diaphragm to pull air in and push air out strongly. Proper posture involves sitting up straight, at the edge of your seat, keeping your shoulders relaxed and releasing any tension in your body. A loose body will help you play more efficiently.
Memorize all of the major, minor, pentatonic, blues, octatonic and whole-tone scales. Major scales consist of the notes found naturally in a key signature. Minor scales have several forms, including harmonic, natural and melodic minor. Blues scales are major scales with an extra lowered third, seventh and sometimes a fifth. Octatonic scales consist of alternating half and whole steps while whole-tone scales consist of all whole steps.
Practice improvising melodies by creating chord progressions that fit with the melody. In most jazz music, the chords will already be written out above or below the melody. In cases where chords are not written out, create your own by keeping common tones between the chords and matching at least one chord member to the melody. For instance, if the first two beats of a melody have the notes E and G, you could have an E major chord on the first beat followed by a C major chord on the second beat since both chords have the common tone E and fit the melody notes.
Use the chord progressions you created to improvise around the melody. Play chord tones on the main beats and insert non-chord tones on off-beats. A non-chord tone can be any note that doesn't fit into the chord.
Practice strength building exercises on your instrument. On piano, play five-note finger exercises that help to develop finger independence. Play one note at a time in each major scale and concentrate on controlling your fingers by only moving the fingers necessary to play tones. On brass and woodwind instruments, practice playing arpeggios and slurs, slowly increasing your speed.