Before beginning this lesson, it's important to understand some things about playing an alternating bass pattern with the thumb or your right hand (if you're right handed). It's one of the most difficult things to get the alternation pattern of C/E/G/E, using the ring finger of your left hand. But once you get it, look out.
The first few measures are structured around the basic C major chord, with a little help from the little finger and an alternating bass pattern with the ring finger of your left hand. Use your right thumb to maintain the bass pattern and whatever fingers that work best for you for picking the melody. I usually use the middle and ring fingers of my right hand.