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.
Fingerpicking Pattern 3
Melodies in minor keys often contain notes from more than one type of minor scale. The key signature for the key of A minor is the same as C major i.e., it contains no sharps or flats. If there are any extra sharps (i.e., raised 6th or 7th degrees) they are written in before the note to which they apply, rather than being in the key signature. The melody of this English folk song contains an F# in bar 8 which comes from the melodic minor scale. All the other notes come from the natural minor. The abbreviation rit. above bar 18 tells you to gradually slow down.