Palm muting is a widely used technique, but hard to get down when you first start playing. It's popularly used with power chords to get a "beefy" sound. Anyways, on with the lesson. When palm muting, it's important that you keep the notes clarity. That is, don't make it so muted that no one (including you) can tell what note you're playing. Start by putting your pinky finger right in front of the bridge across the bottom 3 strings (E, A, and D). Hold an E5 as shown below and strum about 5 times.
I've found in my playing that using your pinky is the best way to palm mute when standing up, mostly because it gives you more freedom of movement, but of course that's just me personally. You can use your actual "palm" when using this technique though.
All right, that's it. Practice, switch up some chords, make a hit riff for a song. Good luck.