Cut or poke a small hole in the bottom center of an empty cardboard or plastic cylinder, such as an oatmeal container or a frozen-juice container.
Cover the cylinder with fabric or paper glued in place.
Carefully push one end of a dowel or long stick into a plastic-foam egg or ball that fits easily inside the cylinder.
Cover the egg with a knee-high stocking. Use a rubber band to secure the stocking under the egg and against the dowel.
Paint features for the puppet, or glue on felt cutouts and cotton balls.
Use a sturdy rubber band to attach one edge of a bandanna or a large square of fabric to the top of the cylinder. Cover the rubber band with ribbon glued in place.
Push the dowel down through the hole in the bottom of the cylinder.
Attach the opposite edge of the bandanna, one or two inches in from the border, to the dowel near the ball. Use the edge of the bandanna to cover the rubber band.
Hold the cylinder in one hand, and hold the dowel (below the cylinder) in the other hand. To make the puppet hide in the cylinder or pop out, move the dowel down or up.