I'm not an expert in jazz music, but I will explain the basics of the blues scale. If you want to see more information about the blues scale on this page, send me your knowledge.
The blues scale
Below is the blues scale based on the note C:
That does not remind you of something? The blues scale looks like the minor pentatonic scale:
Minor pentatonic scale
Blue note is a music note added in the scale. Blue note is a passing note and a dissonant note:
How to use the blues scale?
You can use the blues scale on all chords, like with twelve-bar blues (famous chord progressions in blues music). Don't matter if the melodic notes are dissonant, blues music is dissonant.
Improvisation with a blues scale
I'm not an expert in jazz or in blues music, but I've made for you a small improvisation with a blues scale and on twelve-bar blues:
Transpositions of the blues scale
Below are some transpositions of the blues scale: