In the key of C major the relative minor would be Am. You would write out the Am by starting with the A note in the key of C major. Notice that like the key of C major, Am has no sharps or flats. This is how they share the key signature. And how they are related to each other.
All major keys have a relative or natural minor.
Now here is how you construct the harmonic minor. To construct this minor scale you just take the natural minor and raise the seventh note. The notes of the natural minor of A are as follows. Now look at A harmonic minor. One more example in G major.