Most babies will naturally pull off the breast or fall asleep at the breast when they are full. Sometimes this presents an opportunity to burp and change the baby, after which the baby is ready to nurse on the other side. However, it is not necessary to nurse on both sides at each nursing session. If baby is truly snoozing and not interested in taking the other side at one nursing session, just remember to offer that side first at the next nursing session.
If baby falls asleep at the breast but still has a death grip on your nipple, gently insert a finger into the corner of his or her mouth to break the suction, then remove the breast.