I'm not sure I'm the best person to answer this, since I'm only just a beginner on improvisation myself, but based on my very limited experience, it can be helpful to get familiar with the basics of jazz chord notation first, and then practise arpeggios of the chord sequence that you are going to be improvising over. (I found a Wikipedia article on chord notation that helped demystify it for me, but I'm sure there are probably books out there which would do the same thing.) After a while, you start getting a feel for what notes will sound best, and then you can start playing around with how you combine them.
My teacher has suggested learning by heart some very basic riffs based on the arpeggios, so that I can fall back on those when inspiration fails to strike. This seems to work provided that I remember that they are just a back-up / framework, rather than being a pre-prepared solo, which rather misses the point
Another practising tip he has given me is putting together a basic rhythm for the solo, which then means that I'm only having to select the pitches.
Frankly, though, nothing beats volume of practice. I'm having to make do with CD backing tracks except in lessons (though I agree with TSax that live accompaniment is better), and if I'm having problems, I tend to set the "solo" section of the track on repeat and just keep trying out different things until I relax into it and find something which sounds good. Sorry if that's not very scientific