Measure and cut two 12-by-30-inch sections of 1/4-inch plywood. These will become the hamper side panels. Measure and cut two 17 1/2-by-30-inch sections of 1/4-inch plywood. They will become the hamper's front and rear panels.
Measure and cut a 12-by-18-inch section of 1/2-inch plywood. This will make up the bottom of your hamper. Measure and cut a 12 1/2-by-18-inch section of 1/2-inch plywood. This will make up the top of your hamper. The added 1/2 inch will allow for a lip on the lid.
Place one side panel flat on a table. Apply wood glue to both edges of the top of the panel (not the cut edge). Press the front and back pieces onto the glue. Ensure all lines are matching up and are even. Stand the three-sided frame up on its end. Nail finishing nails every 3 inches along the outside of the side piece into the ends of the front and back pieces to attach the pieces securely together. Add wood glue to the edges of the other side panel and press it onto the open side of the frame. Nail finishing nails every 3 inches until secure. You should have a tall box shape. Wipe off excess glue with a cloth.
Lay the frame on its side very gently. Add wood glue to the entire bottom perimeter edges. Place the bottom section of 1/2-inch plywood into the glue. Ensure all edges are lined up evenly. Nail finishing nails along the perimeter every 3 inches to secure. Wipe off excess glue with a clean cloth.
Stand the hamper up, open end up. Line the top lid section up with the top of the hamper. Back corners should be perfectly aligned with a small lip overlapping in the front. Place the hinges 3 inches in from the left and right rear edges and attach them to the back piece and the lid with a screwdriver, using the appropriate screws. Ensure the lid opens and closes smoothly.
Add decorative trim and handles if desired. Paint, stencil or stain as desired.