Melodic Minor Scales The Minor Scales  (musictheory.net) Theory Things   William Wieland
To write a melodic minor scale, first write an ascending and descending natural minor scale.
On the way up, raise the 6th & 7th scale degrees a step.
On the way down, lower the 6th & 7th scale degrees a step to their original pitches.
(The descending melodic minor scale is the same as the natural minor scale.)
To really learn these scales, sing them, perform them on your instrument and at the piano.