The ability to play blues piano is usually not expected of beginning pianists. There are reasons why most beginning pianists start out playing old songs written by classical composers from centuries past. Many songs written for the piano by such composers as Mozart, Beethoven, and Tchaikovsky were originally intended as pieces to be used for lessons. Plus, the conventions of classical music lead to chord structures, harmonies, and melodies that were comparatively straight-forward, perfect for students who were not musical experts.
Attempting to play blues piano presents new challenges for pianists. Many non-musicians don't realize the technical difficulty of blues and jazz music, but in fact, to be an accomplished musician in one of these genres requires years and years of intense training and practice. Some would even say that these musical genres are actually more complicated than pre-20th century musical forms, which would mean that blues and jazz musicians are, in general, the most accomplished and versatile musicians out there.
So, as you can guess, the decision to take the plunge into playing blues piano should not be made lightly. In order to have a true understanding of blues, its scales, harmonies, and rhythms, one needs to have at least a basic understanding of more traditional musical forms. Blues isn't a parallel form of music to Classical and other traditional genres; no, it's an augmentation of traditional music. Just like jazz, blues actually complicates traditional music. Thus, your study of blues piano requires at least a solid bedrock of musical knowledge.
I presume that you already know, at the very least, about the traditional major scale. For example, in order to understand and play the C blues scale, you must know the C Major scale.
If you have that knowledge, then it's pretty simple. The blues scale simply takes the major scale and adds three extra notes. That's it. The three extra notes are a flatted third, a flatted fifth, and a flatted seventh. Thus, the C blues scale has all of the same notes as the C Major scale -- that is, C D E F G A B -- with the three additional notes being E flat (or D sharp), G flat (or F sharp) and B flat (or A sharp).
That's right, if you look closely at the blues scale, you'll find that there are only two notes that are not included. In the C blues scale, only C sharp and G sharp are not played.
If you want to play blues piano, learning the blues scale is your first step. Even doing nothing more than playing the scale, you'll hear a "bluesy-ness" to the scale, and if you are a fan of blues, it will sound great to your ears.
Once you can do this, you are ready to play blues piano. The next step is to try improvising. Come up with a chord progression. C F G C is a standard blues chord progression, except -- and here is another important point -- it is fairly standard in blues music to turn nearly every chord into a seventh chord. So, this progression, in blues form, would be C7 F7 G7 C7. Of course, with the new notes added in, you must remember that, in most cases, these should be played as minor 7th chords. Thus, both the C7 and F7 chords use notes that are not in the traditional C Major scale.
Once you have your chord progression down, improvising is easy. Come up with a simple, bluesy melody, and go from there. Just remember that in order for the music to have that special blues quality, you need to utilize those extra three notes that are not in the traditional scale. Those are the notes that give blues its edge. In that light, it's really not difficult at all to play blues piano.