Mute / Plant
There is no special way to notate a mute. Look at the rhythmic portion of the sheet music (usually above the tab) for a rest symbol. That is when you should mute the string(s).
A mute (left hand) or plant (right hand) is a technique used to stop a string or multiple strings from ringing.
Mute (left hand)
Place any left finger on the string without pressing down to the frets to stop it from ringing. If a finger is already pressing down on the string, remove pressure from the strings, without removing your finger from the string completely.
Plant (right hand)
Place any right finger on the string in the position you use to prepare for a pick to stop it from ringing.
There is no continuation to this technique.