Watch the Substitute Relative Minor online guitar lesson by Vicki Genfan from Acoustic Rhythm Survival Guide
A relative minor can be used as a substitute for any major chord. This works because the two chords have many notes in common, but a different root. You find the relative minor by counting 6 notes (or 4 and a half steps) up from the note that names the major chord. For example, A minor is the relative minor of C major (C-D-E-F-G-A).
I love using relative minors not only as substitutions, but I will sometimes start playing the major chord and then switch to the RM at the halfway point. This is a really nice effect and adds additional movement to your progression.