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 non-classical 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.
When playing music in minor keys, it is common to use notes and chords from all three types of minor scales. Here is an example; this one also contains one chromatic note (A# or Bb) as part of a repeating bass run.