The hand posture for palm muting is really no different to the standard posture, except that your palm rests on the strings at the bridge to create the muted sound.

For this exercise, simply strum a power chord with all down strums and alternate resting the palm for the mutes, and then slightly lift it to allow the strings to ring.

Get Creative:

Once you can play the 3 exercises as shown in the video, try different patterns, different tempos, and different chords.

Once you are fairly proficient a the technique, find some songs that utilize it. Learn, memorize, and play those songs to develop the technique further.