Cut one of the larger sheets of plywood diagonally to create two triangles for the sides of the cart. Cut the two-by-four into four equal lengths.
Place the 2-by-4-foot sheet of plywood flat on your work space. Put two of the sections of two-by-four on top of the plywood, along the four-foot sides. The two-by-fours should be on their wider side, following the edge of the plywood sheet as closely as possible. They should both cleanly match the edge of one of the shorter sides of the plywood sheet, where the 2-by-2-foot sheet will be nailed on.
Nail the two-by fours to the plywood sheet. If you are concerned that they will come loose, flip the plywood sheet over and also nail through the plywood sheet into the two-by-fours.
Lay the 2-by-4-foot sheet of plywood on the work surface with the attached two-by-fours on top. Place the 2-by-2-foot piece of plywood against the 2-foot side of the 2-by-4-foot sheet of plywood to form an L shape. Nail through the 2-by-2-foot sheet of plywood into the ends of the two-by-fours.
Place each of the two pieces of triangular plywood against the sides of the L-shape to enclose the sides of the cart. Nail through those pieces of plywood into the two-by-fours to attach them.
Put each of the other two-by-fours into the corners formed by the 2-by-2-foot sheet of plywood and the triangular sides. The two-by-fours will extend up past the height of the cart on each side, and will act as handles. Nail them in place well, attaching them to each piece of wood they come in contact with.
Flip the cart over and screw the caster wheels to the bottom (longer side) of the cart, within a foot of the corner. Make sure you are screwing through both the plywood and the two-by-four that runs along the length of the side.