It's a combination of using the left and right hands that has to be learned over time. Basically, you have to be aware of any extra noises that the strings are making, and use any part of your hands that are free, to mute them. For instance when you bend a note, you also use your pinky and thumb of the left hand to mute the other strings.

Once I get my video lessons up and running I'll be doing a tutorial on this kinda stuff. You might also check some of the other instructors cause I'm sure somebody's already done lessons on this.