In Classical music, a melodic minor scale has the 6th and 7th notes sharpened when ascending and returned to natural when descending. 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.
Here is the full fingering for the A melodic minor scale in the open position, up to the high A.