All chords are based on triads, and that is why they are so important. A triad is a group of 3 notes which can be major or minor.

Major and minor triads both use the 1st, 3rd and the 5th degrees of the scale, however the major triad uses the major 3rd and the minor triad uses the minor 3rd. Lets use A as an example. The scale of A Major is
A B C# D E F# G# A and the scale of A Minor is
A B C D E F G A. We are only interested in the 1st, 3rd and 5th so we take those notes and play them together. In A Major this would be A C# E and in A Minor this would be A C E.

This is how chords are formed. Lets look at the chords of A Major and A Minor...

A Major
e|---0-E---|
B|---2-C#--|
G|---2-A---|
D|---2-E---|
A|---0-A---|
E|---------|

A Minor
e|---0-E---|
B|---1-C---|
G|---2-A---|
D|---2-E---|
A|---0-A---|
E|---------|

In the A Major chord we have A E A C# E. These are the notes of the A Major triad with A and E doubled up. In the A Minor chord we have A E A C E. These are the notes of the A Minor triad again with A and E doubled up. This is how all chords are formed.

Always remember that the 1st degree of the scale (A in this case) must always be the lowest note played in the chord, unless it is a slash chord.