One of the coolest things about guitar is the range of expression and texture you can get out of such a simple device. If you think about the differences between the styles of George Benson, Steve Vai, and Noodles (the guy from Offspring), it is amazing that they all call themselves guitarists.
When you push down the damper pedal on a piano, all notes you play continue to sustain until you lift the pedal. It creates somewhat of a "washy" or "ethereal" effect. Recreating that effect on guitar is much more of a challenge. I like it because it's different. Musical. Since pianists do it all the time, the sound itself is quite familiar to the ear, though we hardly ever hear guitarists do it.
The basic idea is switch strings as often as possible. That way, you can leave one note ringing while sounding the next one. Susatain each note as long as possible. Leave each note ringing until you need either the finger or the string to continue the passage.
Besides the obvious finger stretches involved, one of the biggest challenges is to get used to what the licks "feel" like to play. You feel your fingers playing one way, and the sound that comes out of the guitar doesn't quite jive with the message your fingers are sending to the brain. Repetition will cure that inequity. Just do it over and over till you get it.
Here are some examples:
