Playing notes on a single guitar string using alternate picking is one way to play really fast guitar licks. This lesson covers one such example and is played on the G string only. You could use the same approach on any string though which is good for versatility.
This technique relies on moving horizontally on the guitar neck, descending in this instance, and since you do not have to move to any adjacent strings it makes it easy to play the lick really fast. Essentially, less motion means more speed.
Sticking with just the guitar string notes from the G Major scale, the pattern repeats each sequence of three notes, twice. For instance the lick starts in the 12th position and goes: B, A, G and again B, A, G. That is the repeating pattern to use for each group of notes. This means that the intervals are remain diatonic to G Major but you can use this kind of picking pattern in any key you want.
Next we shift to the 11th position and play: F#, G, A and repeat those notes once again. The next sequence shifts to the 9th position and goes: G, F#, E repeating the notes. Now move to the 7th position and play: D, E, F# twice.
Now move to the 5th position and play: E, D, C twice. Shift to the 4th position and play: B, C, D twice. And finally move to the 2nd position and play: C, B, A twice. The last note is an open G staying on the third string.
As you can see each one of these guitar notes are right from the G Major scale. Since this guitar lick is all played on one string, you can really get to playing it fast. Use alternate picking (down up, down up) to get the most speed out of this lick. If you use some picking hand palm muting then you can get a cleaner sound from the strings as you are playing.