Much of my exploration on improvisation is directed towards two types of people: Those, like me, who have an extensive classical training who want to get a grip on improvisation based on what they already know; and those who might be absolute beginners to the joys of playing an instrument (the kinds of people I usually teach) who need to know that improvisation is not something you do only after you've licked the boots of all who came before you.
• how to improvise tonal music in any style: jazz, classical, emo, whatever. i.e., what to do with all those pesky scales you've been learning, without necessarily thinking solely about scales.
• a jazz improvisation primer I made up for some sixth graders I was teaching back in 1997.
• a jazz improvisation primer based on notes from a jazz history class I took at The Boston Conservatory with Jeff Stout in 2000.
• a free improvisation primer I made up just cuz in 2003.
• a rather basic primer on comping bass lines, geared towards folks who know their chords and scales already. This is actually good practice for everybody who doesn't play bass, too.
Also see the open instrumentation pieces I have on my composition page; most of those also contain opportunities to improvise that should be comfortable for those new to improvisation.

I also recommend the following books:
• Doug Goodkin, Now's the Time. Jazz through an Orff Schulwerk lens with some great insights. Don't let the xylophones and metallophones fool you; this is a serious jazz pedagogy book. The material is easily adaptable to any instrument. The strength of the book is that, using African-American musical history pre-jazz, he walks you through fundamental rhythmic and stylistic elements essential to jazz.
• Christopher Azzara and Richard Grunow, Developing Musicianship through Improvisation. Jazz through a Music Learning Theory (Ed Gordon) lens. This book starts with just tonic and dominant harmonies in major keys. If you don't know what that even means, then this is the perfect book for you. If you do know what that means and you're a newbie to improv, this is also the perfect book for you.
• Ed Sarath, Music Theory through Improvisation. Nicole Brockmann, From Sight to Sound. Both of these are geared towards college-level music makers, again usually with more of a classical background.

This page features recordings of me improvising. Enjoy.