Form a rectangular box with the two 1-by-4-by-8 1/2-inch plywood boards and two 1-by-4-by-19-inch plywood boards. Apply glue to the edges of the plywood boards to secure the push cart frame together.
Remove excess glue with a damp cloth. Add extra security to the boards by nailing them to each other with the 4-penny finish nails.
Attach with wood glue the 19-by-10-by-1/2-inch plywood board to the wooden frame to form the bottom of the push cart. Remove excess glue and secure the bottom of the frame with nails.
Turn over the push cart. Select a drill bit approximately the same size as the casters. Drill a hole in each of the four corners of the push cart. Insert and secure the casters to the cart.
Attach the 1-by-2-by-10-inch board to the two 1-by-2-by-18 1/2-inch plywood boards with wood glue. Form a U-shape with the boards to create the handle for the push cart. Add nails for extra security.
Position the push cart upright. Attach the metal push cart handle to the cart according to manufacturer's instructions.