Okay, this is going to be one of those topics where you don't get any nifty new theory stuff or cool licks with which to amaze your friends. In fact, there won't be any theory or technique involved whatsoever.
So why bother? Because in this lesson, we're going to strike right to the heart of the matter. We're going to look at the central issue involved in improvisation: hearing something to play and then playing it! Even if you consider yourself an experienced player, you may never have truly dealt with this issue before. Warning: you may find this a bit discouraging.
Here's the first step: play a chord on your guitar. It doesn't matter which chord; don't even think about it too much. Listen to the chord for a little while, then sing a short (five or six notes, max) melodic phrase that you think sounds good over the chord. Whatever you may think of your vocal abilities, it is important to actually sing the phrase; you need the experience of really hearing the phrase out in the air in the real world as opposed to imagining it.
If you're like quite a few people, you may find that you have some trouble even coming up with a decent-sounding phrase that makes sense to you. If that's the case, take heart; you've just arrived at a very important moment of self-realization and possibly saved yourself a lot of future backtracking, frustration, etc.
Here's the deal: if you're having trouble coming up with a very short melody to sing over one chord, then why would you be worrying about alternate harmonizations for turnarounds or "Coltrane changes" or mixolydian modes or any other stuff like that? You have just identified a very basic deficiency that's going to have to be remedied before any amount of theory or technique will be truly useful to you! Notice that we haven't even talked about playing your idea on the guitar yet. That's because I believe music has to exist inside a musician first. Once we've found some music to express, we can use our instruments to express it.
If you're finding it very difficult to even make up a short melody, don't despair. First of all, relax! I find that many students get a little panicked when confronting this issue ("Oh my God, I'm not actually hearing anything! All my enveloping figures from improv class aren't helping me here!"). So take a few deep breaths, maybe even a short break. Remember this: if you wanted to be a musician in the first place, you're hearing music somehow. It might take a little extra work to get at it but it's in there somewhere. Also, make sure you're listening to lots of music in your life. Listen very intently. Pay extra attention to music you really like and try to make up music of your own that sounds like it. And whenever you find yourself hearing music in your head, try to acknowledge it; see if you can write it down or play it. As stupid as this may sound, I believe the ability to create music is like a little pet inside your head! You have to feed it and water it and spend some quality time with it in order for it to flourish and be happy.
Once you've found a phrase, try to play it on your guitar. If that's pretty easy for you to do, good. Try playing it starting on different strings, at different positions, starting on different fingers. Try playing the same phrase starting on different pitches. Now you're reinforcing the connection between your brain, your fingers and your guitar.
If you had a hard time finding your phrase on the guitar, you've identified another area for development. You're hearing music in your head, but you're not familiar enough with your instrument to play what you're hearing. This can be remedied with patience and practice. One exercise that really helps here is to practice playing familiar melodies starting on random notes. Example: Grab a note on your guitar at random. Don't even look at the fingerboard. Now play "Happy Birthday" all the way through, starting on the note you've grabbed. How many false steps did you make? Were some parts easier to find than others? You're learning a lot about your ability to hear music. Try it again starting on a different random note. Or pick another tune you're very familiar with and play that one starting on another random note.
This stuff might all sound very basic, perhaps even child-like, but it touches on core skills that have a tangible impact on your ability to truly improvise as opposed to merely trotting out "patterns that work" over chord progressions. It is entirely possible to complete a course of what passes for "jazz improvisation" in many schools without ever having to face the potentially scary issue of what you're actually hearing. If you've never thought about these things, I urge you to give the above exercises a try. Your listeners will someday be thanking you for it, whether they know it or not!