The palm mute is a heavily used technique in metal and rock music. It creates a heavy, chuggy, chunky bass like tone to add some extra oomph to the sound of your music.
To make a palm muted sound, you will gently rest the side of your pick hand against the strings right where they connect into the bridge.
Then, just pick like you normally would. Only now, the side of your hand is resting on your guitar strings.
It's important to not move your hand too far to the right. If you do, you will risk removing your hand from the strings and not getting any palm mute sound.
Moving your hand too far to the left will result in a less bassy sound, create a tin like sound, and you can actually change the pitch of the note you are trying to mute.
If you use a left handed guitar, just reverse the right and left directions just mentioned.
You can mute all the strings, but to my ear muting the lower strings (E, A, D) sound best. Of course, if you have a 7, 8, or 9 string guitar, the strings below the E string are also well suited for good sounding palm mutes.
Watch the following video to see the palm mute being used:
John Taylor - guitar and bass instructor for Mile High Shred.