The relative minor is the 6th of the respective major; for example, A is the 6th of C and so A Minor is the relative minor of C Major. Such a pair shares all the same notes (exact same black and white piano keys) but start at differing points.

This is often depicted with the circle of fifths.

Basic examples:

Major KeyRelative Minor
C MajorA Minor
D MajorB Minor
E MajorC# Minor
F MajorD Minor
G MajorE Minor
A MajorF# Minor
B MajorG# Minor