Stack the three shoeboxes on top of each other. Measure the height of the stacked boxes. Measure the width of the boxes.
Cut the large cardboard box apart, creating four large flat sheets of cardboard.
Cut one cardboard sheet to the measurement of the height of the stacked shoeboxes plus 2 inches. Cut two sheets to the measurement of the width of the boxes plus 1 inch.
Tape the cut sheets of cardboard together to create the dresser frame with masking tape. Attach longs strips of masking tape on the inside and outside of the dresser at all seams for reinforcement.
Place the stacked shoeboxes with lid on inside the dresser frame and mark the top edges of the boxes on the inside frame sides with the pencil.
Create drawer supports on the inside edges of the frame with 1-inch wide sections of the shoebox lids at the marked spots. Attach the supports with masking tape on the top and bottom of the support, allowing the support to securely extend at a right angle from the support wall.
Cut three cardboard strips measuring 4-inches by 2-inches for drawer pulls from the leftover shoebox lids. Attach the pulls to the front of the shoebox drawers with masking tape.
Paint the entire dresser and shoebox drawer fronts the color of choice with the poster paint. Let the paint dry thoroughly overnight.
Insert the drawers in the dresser.