If you compare the A natural minor scale with the C major scale you will notice that they contain the same notes. The only difference is that they start on different notes. Because of this, these two scales are referred to as "relatives": A minor is the relative minor of C major.
The harmonic and melodic minor scale variations are also relatives of the same major scale, so A harmonic and A melodic minor are also relatives of C major.
For every major scale (and every major chord) there is a relative minor scale which is based upon the 6th note of the major scale.
Both the major and the relative minor scales share the same key signature.
To determine whether a piece is in a major key or the relative minor key, look at the last note or chord. Pieces often finish on the key note or the key chord. For example, if the key signature contained one sharp, and the last chord of the song was Em, the key would probably be E minor, not G major. Minor key signatures are always based on the natural minor scale. The sharpened 6th and 7th degrees of the harmonic and melodic minor scales are not indicated in the key signature. This usually means there are accidentals (temporary sharps, flats or naturals) in melodies created from these scales.
This old English folk song is well suited to the Classical guitar. It is in the key of A minor. The melody contains F# and G# notes from the A melodic minor scale. In bar 17 the key changes to the relative major (C major) and then returns to A minor in bar 21. This change happens again in bar 25 before finishing back in the key of A minor. The rit symbol above the third last bar indicates a gradual slowing down of the tempo.