Improvisation is something that occurs worldwide, in every musical culture, so participation in improvisation can't be too difficult (or else it wouldn't happen). Of course, some music cultures have highly sophisticated systems of improvisation, and thus require a great deal of initiation, but they all have one thing in common: improvisation happens on some sort of framework. This framework can be very sparse, or incredibly intricate. The sparse ones are easy to deal with: improvise a fixed pitch system without having to deal with rhythm, or deal with specific rhythmic ideas without worrying about pitch. Work with that for a bit, then combine the two.
If I can provide a general axiom for improvisation, it's this: learn stuff, then try to do something with the stuff that you learn. If you're interested in the lydian mode, set aside a bit of time to work out what's going on in the lydian mode in your own terms. If you're interested in a certain meter, let's say 9, then work on writing and playing in 9. And, hey, you were just messing around with the lydian scale, so you can do some lydian thing in 9 now. Learn about chords, do the same thing. Learn about phrase lengths, forms, dynamics, ranges, techniques, do the same thing. You want to be able to read these concepts on paper to put it into your brain, then take what's in your brain and put it in your hands so you can get it into your ear, putting it back into your brain so that you can put it on paper, have it in your ear, then put it back in your hands.
Or, if I didn't want to sound like a homeless person: the end-goal is to connect all parts of your body to the music, and you do that by feeding music from one part to the other. You've indicated that you don't have much time to spend with your guitar, but as with most things, it's about quality rather than quantity. If you can put yourself in the zone for half an hour every other day to wrap your head around an idea, learn how to hear it, learn how to feel and play it, then you'll build a bond with your instrument and find ways to make it say what you want to say. If you really want to jump-start your playing, joining a band is a good idea. You can find some instructional resources that are very specific when it comes to teaching improvisation, but I believe that what I've said is a good general model for learning music on a personal level.