You can simply learn the chords which "belong" together, or you can learn the "circle of fifths". If you know the circle of fifths, it's easy to find the chords for the blues.
The Dominant chord is based on the fifth note of the major scale: for the key of C, that means the dominant is G. The chord is made up in the same way as all major chords: the base note, the third and the fifth (which gives you G/B/D for the chord of G major). In the circle of fifths, the Dominant is to the right of the tonic, and the sub-dominant to the left. (You don't have to know this, it just makes life a little easier if you do!)