The thumb (p) usually picks the 6th, 5th and 4th strings. Pick with the lower side of your thumb, as shown on the right. Pick with a downward motion and keep the thumb rigid, i.e. do not bend it as you do when picking with your fingers.
Now try this example which combines the use of the thumb and fingers. Once again, take it slowly at first and practice each bar separately until you can produce a strong, clear tone.