This method is very popular in rock music due to the heavy 'chugging' sound it creates. To palm mute, press the strings down firmly with the heel of the right hand and pick with the thumb. Practice on just one note to begin with, then when you feel comfortable, move on to the other strings.
How do you palm mute a bass?
The palm mute is a playing technique for guitar and bass guitar, executed by placing the side of the picking hand below the little finger across the strings to be plucked, very close to the bridge, and then plucking the strings while the damping is in effect. This produces a muted sound.