In the beginner study of the Am, G, Em, F progression, we looked at creating scales to fit the chord changes. In intermediate, we combined the linear approach with the blues approach. Now, in advanced, I introduce chromatics into the mix.
Here are some ways to look at using chromatics to create some real interest in your playing. Take a look at measure 2. There is an Ab in beat 2 which does not fit within either A natural minor or A blues. If you were to just play an Am chord with an Ab on top it may not sound very consonant. The reason it works in this context is because the Ab is used as a passing tone between the A before it and the G after it. Also, the Ab is on an unstressed part of the beat which deemphasizes the importance of the Ab to fit within the chord under it. I use another passing tone in measure 3 when I play A, Bb, B (the Bb is a passing tone).
I used this approach to soloing much more when I got the gig with Steve Morse and the Dregs. I knew that as part of the gig I would be asked to solo over a certain number of bars that may have been over the same chord the whole time. If I only played a blues scale for sixteen measures the solo would get boring very fast. Therefore, I employed the chromatic approach to keep my solos interesting.
Another cool way to use passing tones is to play a repeating pattern. In measures 15 and 16 I cycle chromatically down in thirds. When I finally stop this journey I end up in a more consonant passage which provides relief for the listener!
Generally speaking, whenever you want to include chromatics, try to resolve the passing chromatic tones to the closest scale tone. As you experiment more and more with different approaches you will find the techniques that you like to use most often. You should focus on these and work on creating your own unique sound. Create your own approaches to improvisation.