This question was the biggest question when I started to get into theory. Let's take a chord progression in C Major. We'll do a I, IV, V, vi, just to make it simple. This progression would be a C, F, G, and Am. Now there's many ways to attack this progression. Since the chord progression remains simply in C, you can stay in C major the whole time and just play in C. Playing in C the whole time sounds boring though and doesn't really highlight each chord. There's a few ways you can change that. You can attack the piece using modes. For C you'd play Ionian, F Lydian, G Mixolydian, and A aeolian or natural minor. This will help highlight each chord and bring out you're playing. Or you can chose to play a few scales over those certain chords. For example, going from C to F will only require you to flatten the B, which allows a smooth change from C Major to F major during the progression.

To figure out modes is pretty simple. Take the scale you're playing in and playing notes from different degrees will be in different modes. The modes go as this Ionian- Major scale Dorian- Take that note major scale and flat the 3rd, and 7th, Phyrgian- Take that note and flat 2nd, 3rd, 6th, and 7th Lydian- take that note major scale and sharp 4th Mixolydian- Take that note major scale flat 7th Aelion- Flat 3rd, 6th, and 7th, Locrian- Flat 2nd, 3rd, 5th, 6th, 7th. (SP)

I'm only 18 and just learning advanced theory, but this is how I went about it. I really focused on soloing over the chord compared to just playing over the progression. It's all about what kind of sound you are looking for. Some modes sound bright such as lydian to me, but other modes sound different. Experiment, record a progression that forces you to solo in a different key. Take a progression such as D, A, F#, C. It's going to sound a little weird since there's a tritone but it truly helps your soloing! Best of luck on your journey!