In the A melodic minor scale the 6th and 7th notes are sharpened when ascending and returned to natural when descending. This is the way the melodic minor is used in Classical music. However, in Jazz and other more modern styles, the melodic minor descends the same way it ascends. An easy way to think of the ascending melodic minor is as a major scale with a flattened third degree.
Melodies in minor keys often contain notes from more than one type of minor scale. The song Greensleeves is mostly derived from the melodic minor, but also contains a flattened 7th degree which comes from the natural minor.