How do I improv over chords on guitar quickly?

You can't do anything on your guitar quickly without realizing a couple of very important factors. First and foremost: You can not rush things - ever. Learning to play guitar (or any other instrument for that matter) takes a lot (as in a LOT) of dedicated and correct practice. As soon you start to rush things and want to speed up, you develop poor technique and bad habits - extremely counter productive.

Secondly: in order to do something complex, you need to simplify things a bit first. That usually means speeding things way don and also doing things in chunks. Rather than trying to switch between a whole section of chord changes, you should concentrate on just two chords at the time - going back and forth slowly until you sound good and clean - then and only then can you begin to increase tempo.

You then repeat this process with other chord changes until switching between them is second nature. For the majority of beginners, this usually takes months of good practice routines.

When you have played for a period of time and have the basic chords figured out on the fretboard, you can see a chord sheet for a song - say for instance it is C, F, G, Am, Dm and C - and play those chords without giving it a second of thought as to where you put your fingers ... as long as you use the basic forms of the chords and use regular strumming or finger picking. Doing complex things with your basic chords can of course complicate things at that stage.

So yes, the simple answer is that it just comes with practice - the correct kind of practice.

You can't know quickly, this isn't making instant ramen.

It comes with practice AND creativity. Someone can improv with a torrent of notes, someone else can pick one note and play that single note over four bars over the exact same chord progression, and both can sound amazing.

Don't rush things. Damn people always want to rush things. The only reason other people get it quicker is because they're a musical genius or they put in more time. It's usually the latter. Put in more time every day, and you will get it faster than someone who puts in less time.

You can start with licks. Each famous player has a set of licks and riffs they will always go back to. It's true for guitarists, and bassists and drummers and saxophonists and everyone else. These licks and riffs are always used by a lot of people because they will work most of the time. You can think of it either as an anchor you can always go back to, or as a base to start off from or work upon.

Listen to pop songs. Lots of pop songs. Pop songs are popular because the melodies are very catchy. And you will learn a lot if you dissect pop songs into riffs and hooks and licks that you can work with. Another advantage of studying pop songs is that you can go back in time and you get more complex chord progressions.

find 3 of them and just bounce back and forth for hours.. then change one of them... I did it with E.A.D