Like majors and minors , they consist of three notes from a particular scale , 1st , 3rd & 5th .... You can look at them as two notational intervals (between 1st & 3rd , and between 3rd and 5th) ... Here are the formulas :
Major : Maj 3rd + Min 3rd .... Example : C E G
Minor : Min 3rd + Maj 3rd .... Example : C Eb G
Dim : Min 3rd + Min 3rd .... Example : C Eb Gb
Aug : Maj 3rd + Maj rd .... Example : C E# G#
(I wrote E# instead of F , because F would be the 4th, not the 3rd ... Nevermind anyway)
Maj 3rd = 4 frets , 2 whole steps
Min 3rd = 3 frets , 1.5 step
Here are examples for Aug and Dim chords :
Dim : Edim[x753xx] , Edim [xxx986] (the infamous malmsteen's diminished sweep pattern!)
Aug : Eaug[x765xx]
Economy picking:
It doesn't need any tabs or stuff to demonstrate , I'm sure you've got a plenty of tabs for scales and modes written in 3 notes per string patterns ... All you you have to do is to start each string with a downstroke for ascending and up stroke for descending.
It would look like this :
D U D D U D D U D D U D etc. For ascending
U D U U D U U D U U D U etc. For descending
Personally , I found that strict alternate picking throughout is much practical for me ... You should decide which's better for you.
Hope that helped.