The harmonic minor is often described as having an "Eastern" sound. It has a distance of 1½ tones (instead of one) between the 6th and 7th degrees. The raised 7th degree is the only difference between the harmonic minor and the natural minor scale.
Here is the full fingering for the A harmonic minor scale in the open position, up to the high A. Remember to play notes at the 4th fret with your 4th finger. As with all scales, learn it from memory and then play it with your eyes closed, naming first the notes out loud, and then naming the scale degrees.
This melody is derived from the A harmonic minor scale. Once you can play it, try transposing it up to the higher octave of the scale.
Here is an arpeggio based part in the key of A minor, which uses notes from both the natural and harmonic minor scales. Learn it and then try making up your own parts based on the ideas presented here.