Cut a piece of 1/2-inch plywood to 12 by 12 inches for the seat of your small chair using a circular saw. Cut a second piece of 1/2-inch plywood to 8 by 12 inches for the seat back. Gently sand the cut edges of both pieces of plywood using fine-grain sandpaper.
Use the circular saw to cut four 2-by-2-inch pieces of hardwood to a length of 10 inches. These pieces of hardwood will be the legs for your small chair. Cut four 8-inch lengths of 1-by-2-inch hardwood for the seat supports.
Arrange the four pieces of 1-by-2-inch hardwood in a square, standing them upright on their longest narrow edges. Position one of the 2-by-2-inch legs upright in each corner of the square so the ends of the 1-by-2-inch pieces of hardwood are flush against the sides of the legs.
Align the outside edges of the legs and the seat supports. Drive 3-inch wood screws through the sides of the chair legs into the thickness of the seat supports to secure the frame.
Cut two pieces of 1-by-2-inch hardwood to a length of 10 1/2 inches and a third piece to a length of 8 inches. These pieces of hardwood will be used to construct the seat back support for your small chair.
Place the two 10 1/2-inch pieces of hardwood flat against one side of the chair frame you just finished constructing. Position the pieces of hardwood so they are aligned with the 2-inch chair legs along one side of the frame. The two pieces of hardwood should overlap the frame by 2 inches so 8 1/2 inches extends above the chair seat.
Drive 3-inch wood screws through the 1-by-2-inch pieces of hardwood into the chair frame. Sandwich the 8-inch piece of hardwood horizontally between the upper ends of the two 10 1/2-inch pieces and drive 3-inch wood screws through the vertical pieces into the horizontal piece to complete the chair back support.
Lay the 12-by-12-inch sheet of plywood flat on top of the square seat frame and align the edges. Drive nails from a nail gun down through the plywood into the frame to secure the seat.
Hold the 8-by-12-inch piece of plywood flat against the seat back. The bottom edge of the seat back should sit flat on top of the seat, and the outside edges should be aligned with the edges of the seat back support. Drive nails from the nail gun through the plywood into the seat back support frame to attach the seat back.
Paint or stain your completed chair to match the decor in your room. Alternatively, decorate the chair with stencils and craft paint for a more child-appropriate look.