Here we have a C major scale -


C D E F G A B

If you start at C and take the 1st, 3rd, and 5th notes, you get a C major triad (CEG). If you start at D and take the 1, 3, and 5, you get a D minor triad (DFA). And so forth.

This is how all chords are built. And you can get variations on the 135 format. For example, the dominant 7th chord is built on the fifth tone of the major scale. Start at G and count the 1st, 3rd, 5th, and 7th tones, and you get a G7 (GBDF).

Hope that helps!