Every major key has a relative minor. This means that this minor key has the same notes as its relative major. It will also share the same key signature as well.
When you start on the 6th note of any major scale and play all the notes up to the octave above, you are playing the natural minor. It is also called the Aeolian mode. To find the relative minor of any major key, look at the name of the 6th note in that major scale.
Conversely, to find the relative major of a minor key, go up 3 semitones from the 1st note of the minor key (tonic). Make sure you go up 3 letter names as well so as to avoid enharmonic equivalents. (An enharmonic equivalent is when two notes sound the same but have a different letter name. e.g. C# & Db)
E.g. What is the relative major of G minor? If you go up 3 semitones from G, you might say A#. But you must also go up 3 letter names. This will give you Bb. A# is incorrect as G minor has flats. That is why you must always go up 3 letter names as well.
The harmonic minor is similar to the natural minor but instead raises the 7th note. The accidental of this raised note is not a part of the key signature, but is written next to the note when it appears in the musical score.
The natural minor was adjusted to the harmonic minor because composers liked the harmonies it created in chord progressions that used a V- I. Using the natural minor, the V chord is a minor chord. Using the harmonic minor, the V chord becomes major.
The melodic minor is the third type of minor scale that was also created to provide more options for composers. It raises the 6th & 7th notes in the ascending scale and then lowers those raised notes when the scale is descending.