One of the most efficient ways to memorize scales and play them on the guitar is using box patterns. These are ways of 'mapping' the scale across the guitar fretboard, creating fixed shapes that can be transposed to play the scale in a different key. Once the patterns for the natural minor scale have been memorized, raising the sixth and seventh degrees by one semitone (that is, playing them one fret higher) will give the melodic minor scale as a result.
This will create some fingering differences: below you'll find the graphic representation of all the box patterns for the harmonic minor scale in every key. Select a root note to see a list of box patterns for the harmonic minor scale:
The melodic minor scale is a variation of the natural minor scale in which the sixth and seventh degrees are raised. The harmonic minor makes use of the raised seventh degree in order to create a leading tone to the tonic, but as a consequence, an augmented second interval appears between the sixth and seventh degrees. Common practice composers found this to be a generally harsh sounding leap when it came to melodies, and some considered it unnatural for vocal music. This eventually led to the rising of the sixth degree in order to reduce the interval. Thus, the melodic minor scale's status as a real scale is debatable, as some consider it like a mere variation employed for melody constructing purposes.
The rising of the sixth degree makes the second tetrachord of the scale identical to that of a major scale. It also opens the door to the use of the major IV chord, as well as the half-diminished raised VI chord.