Watch the Arpeggiation: Level 1 online guitar lesson by Chris Buono from Guitar Gym: Arpeggiation
In Workout #1, you'll play open position E and A chords. In the first two bars you'll pick the open E from the bottom to top (6th string to 1st string) with all downstrokes as you ascend the pattern until you get to the top note (open first string) where you'll play an upstroke. This is the beginning of the "surround technique." From there you'll arpeggiate the chord in a reverse fashion - descending the pattern starting with a succession of upstrokes that ends with a lone downstroke on the lowest note once again surrounding the borders.
When playing the A chord in bar 3, you'll once again pick from the bottom to top (this time 5th string to 1st string), but at the end after the surrounding upstroke on the 1st string, you'll play a downstroke for the 2nd fret C#. In the fourth and final bar, you'll start the pattern with that same C# with a downstroke and then descend the chord with all upstrokes until the final downstroke for the open A.
Regarding the A chord in bars 3 and 4: If there's one chord that seems to have a few ways for it to be fingered, it's this one. To be able to play this workout and the remaining Level 1 Workouts, be sure you're fingering the open A just like I do: a 2-3-4 fingering on the 2nd fret of the 4-3-2 strings respectively. This will enable you to make a smooth change from E to A and let you concentrate on the task at hand - picking the chord tones while letting them ring into each other.