Slice straight along the bottom edge of the spout on a half-gallon paper juice or milk carton and cut straight down both sides and along the bottom to form two halves. One half carton is the wagon box so you can recycle the other half or use it for another craft. Cover the wagon box with masking tape to resemble boards or wrap it in brown paper bag.
Cut two cardboard rectangles about one inch wide and tall enough to stick out above the carton edge about two inches. Glue them in the corners at the spout end. Cut two or three more rectangles the width of the carton glue them to the side supports to form a wagon seat and back.
Cut six pieces of wide straw the height of the wagon box. Glue two in the back corner and two just behind the seat (one on each side). Place the third pair opposite one another at the midpoint on the inside edge of the sideboards. Bend 12-inch lengths of flexible coat hanger wire into arches and insert the ends into the straw supports over the wagon.
Cover the arch supports with a sheet of brown paper bag or white cotton cloth. Tie the cover to the wires or glue to the sideboards of the wagon bed.
Trace a plastic container lid four times on thick cardboard. Draw a wagon wheel pattern on one side. You may choose whether to use the cardboard wheels alone or glue them to four plastic lids for a sturdier wheel.
Tape a length of wide straw the width of the wagon bed to the front and back on the underside. Run a thin straw or wire axle through each straw support so it sticks out a little on each side. Hot glue the wheels to the axles.