Firstly, lets take a look at the chords for this first section:
Amaj7 - Amin7 - Gmaj7 - Gmin7 - F#maj7b5 - F#min7
Each arpeggio is based on the chord which is occurring underneath at the same time so over the first chord we have Amaj7 and we play an Amaj7 arpeggio. The arpeggios are played with a combination of left hand hammers 'from nowhere', string skipping and right hand taps. These shapes are extremely useful in that we can but up a considerable amount of speed without too much exertion, which is always handy!
Once you have mastered the actual shapes required all you have to do is move exactly the same shapes down to the corresponding position et voila! One thing you will have to be cautious of is position shifting from one pattern to the next. I always find it useful to look at the fret I need to move to just before I need to move to it. Also, as you descend the frets will become slightly wider so you will have to make some adjustments with your fretting hand. Nothing major but still worth paying close attention to.