This example is a I-IV-I-I-IV-IV-I-I-V-IV-I-V 12-bar blues progression, so you can see that bar 1 is played out of an E chord and bar 2 is played out of a A chord fingering. Bars 3-4 are simply a repeat of bar 2 of the intro, followed by a little E7 plinking, so let's just focus on bars 1-2.
In bar 1, you simply play the low strings of an E chord, then move your pinky to the 3rd fret of the top string and plink lightly several times. Keep in mind that you want to keep the volume on that plinking slightly lower or it could sound a bit obnoxious.
Bar 2 is all played out of A and A7 chord fingerings, all you are going to do is take your A fingering, pick the top two strings individually and let them ring, then move to an A7 and pick them together with some feeling. This move is really simple, and Lightnin' got lots of mileage out of it!