The p finger (thumb) usually picks the 6th, 5th and 4th strings. Pick with the lower side of your thumb as shown in the following photographs. Pick with a downward motion and keep the thumb rigid, i.e., do not bend it like you do when picking with your fingers.
Now try this example which combines the use of the thumb and fingers. Take it slowly at first and practice each bar separately if necessary.
Here is a Blues which uses previously discussed fingerpicking patterns along with bass runs played by the thumb (p). Take it slowly at first and make sure all the notes sound clearly.