Chords are made from arpeggios, which come from scales. I've talked before about the 7 "Church" modes, or Canonical Modes as they are also called: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian. Of those modes, the most commonly used are Ionian (Major) and Aeolian (Relative Minor). The intervals of the Ionian (Major) mode are R,W,W,H,W,W,W,H R=Root, W=Whole, H=Half. The intervals of the Aeolian (Relative Minor) mode (starting on the 6th note of the Major scale), are R,W,H,W,W,H,WW. If you assign each interval with a number, then the notes of the scales will be 1,2,3,4,5,6,7,8 with 8 (the octave) being a repeat of 1 (the tonic or first note). The notes of the arpeggio will always be 1,3,5,8 - regardless of the notes of the scale, or the mode.
G Ionian (Major): G,B,D,G
G Aeolian (Relative Minor): E,G,B,E
Using the example above for the key of G, you want to make up your chord with any of the above notes: G,B,D,G for the Major and E,G,B,E for the Relative Minor.
OPEN CHORDS VS CLOSED CHORDS
One of the advantages of the mandolin is that it can be played like a percussion instrument in addition to providing melody and harmony. The mandolinist has to decide what he/she wants to provide in the way of accompaniment. If the mandolinist wants a short percussive sound (called a "chop" in bluegrass vernacular), then he/she has to use "closed chords". Closed chords indicates a finger on each string, "closing" the ringing of the strings. Every mandolinist has to learn the "Big G", which uses all 4 fingers with fingers on the B (a string), G (e string), G (d string), D (g string). This is a "closed chord" because all of the strings are "closed" by a finger. If the mandolinist wants a sound that rings (like a harp, for example), then he/she will play "open chords". Open chords have one or more string pairs untouched by fingers allowing them to ring when struck by the pick. Using the G example, a good open G is B (a string), and G (e string), open D and open G.
Typical styles of music that use open or closed chords are:
I hope this is helpful, here's the video: