Have everyone sit in a circle.
Ask a volunteer to introduce themselves and the four people on their left to the rest of the group.
Then the volunteer may ask one of the four people he or she has introduced to switch places with anyone else in the circle (except for the five just introduced.) The person who takes the previously introduced person's place must then introduce themselves and the four people to their left.
Continue until everyone is able to introduce everone else. For smaller groups, have kids introduce just one or two people.