Cut four 2-by-3-foot rectangles of plywood on the table saw. Cut one 3-by-3-foot square of plywood. Cut a 3-foot section of the 1-by-2-inch lumber, and cut two 34-1/4-inch sections. Cut six additional 23-1/4-inch pieces of the lumber. Cut two 30-inch pieces of 1-by-2-inch lumber.
Lay the 2-inch face of the 3-foot section on one side of the 3-foot square. Line up the sides of the 1-by-2-inch lumber with the edge of the square. Drill pilot holes through the strip and the plywood every 6 to 8 inches. Drive a wood screw into each hole. Lay the 34-1/4-inch pieces perpendicular to the first piece lined up on the side. Drill pilot holes and secure with wood screws. This is the bottom of the cart.
Secure the 2-inch face of two 23-1/4-inch pieces on either side of one of the 2-by-3-foot rectangles. There will be a 3/4-inch gap at the bottom of the piece. Drill pilot holes and secure these support pieces. This is the front of the cart.
Place the 1-inch face of a 23-1/4-inch along a 2-foot edge of another rectangle, leaving a 3/4-inch gap at the bottom. Drill through the plywood into the support and secure with a wood screw. Place a second support 1 1/4 inch behind the first. Drill pilot holes and secure. Repeat with another rectangle and the last two supports. These are the sides. The final 2-by-3-foot rectangle is the removable back of the cart and remains untouched.
Lay the front piece of the cart perpendicular to the bottom section. Fit the bottom supports into the 3/4-inch gap at the bottom of the support. Drill pilot holes and secure. Turn your work on the side.
Lay one sidepiece to rest on the supports secured to the bottom and front. The back groove lies on top of the bottom support and faces the inside of the cart. Drill pilot holes and secure. Flip the box over and repeat with the other side. Place the box on its bottom, and slide the back piece into the grooved slots.
Lay the yardstick diagonally across the side of the box, and draw a line with a pencil. Draw a line diagonally the other way to find the center of the box. Measure 2 inches toward the back from the center point, and make a mark.
Place the yardstick on this mark, and draw a line from the top of the box to the bottom. Measure 8 inches below the mark on the line, and drill a pilot hole to mark the spot. This is where you will put your wheel. Placing the wheel slightly behind and below the center balances the cart and gives you clearance for the wheels.
Measure the distance from the hole to the top of the box and from the hole to the front of the box. Cut a rectangle to fit these measurements.
Lay the box on its side. Lay a shovel handle flush with the top of the box so that the handle extends beyond the front of the box. Tape the handle in place to hold it temporarily. Lay a 30-inch length of 1-by-2-inch lumber along the front edge on its 1-inch face. The bottom of the piece extends below the bottom of the box.
Drill pilot holes and secure. This is one of the stands. Place the rectangle on top of the shovel handle and the stand, lining up the top and front edges. Drill pilot holes along the front edge, and secure with wood screws. Drill four evenly spaced holes through the rectangle, shovel handle and side. Push a bolt through the hole, and secure with a nut on the inside of the cart. Repeat with the other side.
Remove the back section of the cart. Drill a 3/8-inch hole through the pilot hole drilled earlier. Continue to drill through the rectangle. Slide the bicycle wheel into the space between the rectangle and the side of the box. Push the 3/8-inch bolt through the rectangle, axle and side of the cart. Secure on the inside with a nut. Repeat on the other side.
Lift the cart onto its wheels. Rest the cart forward on the stand.