Get acquainted with your horn until you find your way around the keys with fluidity and speed, which are two critical components of the improvisational equation. The less time you're fumbling around, the faster you can react to what happens on the bandstand.
Understand how music is created, and the scales required for each specific musical situation. Western music is based on the 12-tone scale, but jazz improvisation is built around seventh scales--leaving you seven notes to deploy. This means some notes will work less well, such as the fourths and sixths more commonly associated with classical music.
Start by memorizing blues scales--which are built around the flatted first, third, fifth and seventh notes--and provide the foundation for boogie-woogie, R&B and funk styles. Learn the relationships between the notes of each scale as you master it. For example, blues scales are based on I-IV-V chord patterns, or the first, fourth and fifth notes.
Buy an instructional CD that allows you to play horn lines off bass and drum backing tracks--it's a great way to get your feet wet before jumping into the fire with a real band. Record your practice sessions, too, to get a better feel for building solos and resolving notes.
Learn the difference between scales and modes--which are typically built around the root notes of a major scale--and are handy for soloing over fast-moving chord changes. However, scales remain the preferred improvising method, because you won't always want to start soloing on the root note of a chord--and not all changes lend themselves to the modal approach.
Approach solos as a melodic statement with a beginning, middle and end--don't bang out a bunch of notes that have nothing to do with each other. This is where knowledge of chords, keys and how they work together is critical--especially in jazz, where chord sequences change rapidly and dramatically.
Realize that "less is more"--great artists like tenor saxophonist John Coltrane practiced this principle throughout their careers. Playing fewer notes and phrases gives the music breathing space, creating room for a tension and release that opens greater scope for individual expression.
Don't fret whenever you blow a wrong note (or "clam"). Try to regroup by blowing chromatic phrases or passing tones (so called, because they help you get to the next note). If you can't recover, don't beat yourself up--learning on the bandstand is rough at times, but there's no better place to do it.