The blues is one of the oldest and most played forms of jazz. For must beginning improvisers, it may be your first exposure to improvising. In a school jazz band, it's the blues that's most often "opened up" for solos. That's because everyone things that playing the blues is easy. On the surface, when someone says "just play a blues scale", yes, it's only 6 notes, so on the surface it's very simple. And the form is simple, with only three or four chords. I also believe that the blues scale is an important tool. Everyone uses it. But I do want you to not stop there. The nice thing about using a blues scale is that you can use the same scale for the whole progression. This is a boon, but it has it's limits, too. I've found that if you aren't conscious of the form, then your solos wander, and you don't know where to start or end. Therefore, the first exercise is to count the measures of a blues. Most blues have a 12 bar form, so count along with the track... 1-2-3-4, 2-2-3-4, 3-2-3-4, up to 12, then start again. You should be able to hear and feel the form after doing that a few times. This is important, so don't skip this step, even though it might sound elementary and silly!
Now, here's your first step, the blues scale. This varies a lot from any scale you might have played in the past. It's not major or minor or dominant, and based on "blue notes" Blue notes were a part of the very earliest parts of jazz, before it was even jazz. Blue notes came from Africa, and were brought here by African slaves. Please go to these links for more information on the history of Congo Square and blue notes. Congo Square is now a part of Louis Armstrong Park in New Orleans. Here is a nice technical explaination of the blues.
Take a few minutes to memorize this scale, then play along with the track. You will find that this scale automatically sounds bluesy and funky. Just remember this is only your first step. Make sure when you improvise to play something that makes sense and tells a story, not just random notes
Feel comfortable with the blues scale? Good! Now let's get more in depth with the blues.