I cut shapes out for ears, noses, eyes, paws..use different colors of paper or they can color them in. The love to glue! I wanted to have some different shapes so they could choose any animal. I cut the mane out for the lions by just making it bigger than the head and they glued the ears on from the back of the head before gluing on the mane.
Cutting the eyes and stuff out gives them a chance to make up the animal, or person, that they want to make. I keep a bin of markers on the table for the rest of the design.
I folded a piece of paper so there was a pleat in the back. I then cut it so it was smaller then the front with the pleat in the center. Glue the outer edges to the back side of the puppet front and let dry. These have held up to a surprising amount of play.