Watch the 6/8! online guitar lesson by Angus Clark from Essentials: Rock Rhythm Unplugged
Before addressing the nitty-gritty here, I want to point out that this lesson is an extension of the lesson about using ringing open strings as common tones across chord changes. Now that we're in E minor as opposed to A or E major, we can use the open G, B, and E strings to great effect.
Lessons in this example: Position shifting and reducing string noise, right hand accuracy, strumming in 6/8, and dynamics with the pick.
HOT TIP: Tailor your arpeggio pattern so that you hit an open string as the last note before a chord change so that your left hand has extra time to plant itself on the new chord. This strumming example is another reminder to keep the strumming fairly even, without a lot of upstroke accenting.
Performance Tip: In the transition from the arpeggio section to the strumming, pick a bit more authoritatively in order to set up the transition.