Here is a breakdown of the scale as it compares to the regular minor scale;
A - B - C - D - E - F - G
A melodic minor:
A - B - C - D - E - F# - G#
If you are familiar with modes, you also have modes with this scale as well. If I were you, I would start with this scale and get familiar with it's shape and sound. Once you get it under your fingers, than figure out where it applies in jazz. For that, there are certain chords which are ever present in jazz where this scale could be used. Before we get into all that, try and get this under your fingers first and than let's take it from there.
Feel free to correspond with me about this via my "Ask Douglas Showalter" thread, and let's work to help you understand this great concept.