| For the most part, triads are three notes (duh) with a third between each of them. So, in general:
note - interval of a third - note - interval of a third - note
OK, what's a third? The distance between two notes that's more than a second, which is one or two half-steps, and less than a fourth, which is five or six half steps. A third is three or four half-steps, the distance between, say, C and Eb (minor third), or C and E (major third).
With me?
So, there's just a few triads. Since there's two kinds of thirds (major and minor), and there's two thirds in a triad (the distance between the first note -- the root -- and the second note, and the distance between the middle note and the top note), we can arrange all of the possible combinations like so:
m3 m3 (small m for minor): C Eb Gb (C diminished)
m3 M3: C Eb G (C minor)
M3 m3: C E G (C major)
M3 M3: C E G# (C augmented)
It's not quite that easy, though, since you can invert the triads which simply means to rearrange the notes: Eb Gb C is still C diminished.
I hope that's what you were asking for. Try looking at Mick Goodrich's books, like The Advancing Guitarist or that harmony almanac thing he created. He has a system for understanding all of jazz harmony based on triads (rather than seventh chords, like usual). | 
