P.o.A, I'm pretty much where you are in terms of going from a familiarity with rhythm to wanting to learn what soloing is about.
Take my advice with a grain of salt because I'm still learning everything much like a novice....but....
Master the scales. Start with the pentatonic and then branch out to the others...moving onto the the major and minor scales. Soloing is mainly understanding scales and how they fit in over top of chord progressions. This means that also knowing a bit of theory will go a long way. Martian will back me up on that one!
So if you aren't already doing it, bring in some serious scale drills into your practice. It will both get your fingers up to speed and nail into your head the patterns you can use to solo, even as improvisations! All you would need to know is the chord progression and then off you go. This advice also applies to picking up intros, riffs, turnarounds, outros, etc.... It's all related somewhat.