Arrange two of the 22-inch pieces of 1-by-4-inch hardwood and the two 24-inch lengths in a square shape. Position the four boards upright on their longest narrow edges and sandwich the shorter boards between the longer two. The result should be a 24-by-24-inch square frame.
Secure the frame by driving 2-inch wood screws through the longer boards into the shorter ones. Slide another 22-inch length of hardwood into the frame, parallel with the other two boards of the same length. Adjust the board so its inside edge is 5 inches from one of the parallel boards and screw it in place.
Stand the remaining four 22-inch pieces of 1-by-4-inch hardwood upright on their shortest narrow edges in two pairs. Lay one of the 27-inch lengths of 1-by-4-inch hardwood flat across the top edges of each pair of boards.
Align the outside edges of one of the 22-inch boards with the 27-inch board at one end. At the other end, position the boards so the 27-inch piece overhangs the 22-inch piece by about 1 inch. Drive 2-inch wood screws through the 27-inch board into the 22-inch boards to secure them. Each of these structures will serve as a pair of chair legs.
Stand the two structures you just completed upright. Hold the 27-inch piece of 1-by-2-inch hardwood flat against the 1-by-4-inch boards so the top edge is positioned under the 1-inch overhang. Attach the 1-by-2-inch board by driving 2-inch wood screws through it into the 1-by-4-inch boards.
Lay the square frame you constructed earlier flat on the ground and position the structure you just completed over top of it. The inside edges of the vertical 1-by-4-inch boards should be flush with the outside edges of the square frame.
Adjust the square frame so the outside edges are roughly centered on the widest part of each of the four chair legs. The side of the square frame where you installed the additional 22-inch length of 1-by-4-inch hardwood should be at the back, nearest and parallel to the piece of 1-by-2-inch hardwood connecting the two pairs of chair legs.
Raise the square frame so the top edge is about 12 inches off the floor. Attach the frame by driving 2-inch wood screws through the 1-by-4-inch chair legs into the frame. The resulting structure will serve as the basic frame for your slat chair.
Arrange the five 20-inch lengths of 1-by-4-inch hardwood flat on top of the square frame to serve as the seat slats. One edge of each board should be aligned with the additional 22-inch board inside the square frame, and the other edge of each board should slightly overhang the front of the chair frame.
Adjust the boards so they are approximately 1/2 inch apart. Screw the seat slats down by driving 2-inch wood screws through the boards at each end into the square frame below.
Lay the five 22-inch 1-by-4-inch boards parallel to each other with their ends aligned. Space the boards about 1/2 inch apart. These boards will serve as the slats for your seat back.
Lay the three 20-inch pieces of 1-by-2-inch hardwood perpendicularly across the width of all five slats. Arrange the 1-by-2-inch boards so one is about 3 inches from each end and the third is halfway between. Attach these boards by driving 2-inch wood screws through them into the seat slats.
Place the completed seat back inside the chair frame with the 1-by-2-inch boards facing down. Position the seat back at an angle so it leans against the seat back support and the bottom edge of the seat back butts up against the seat slats you already installed.
Drive 2-inch wood screws through the horizontal piece of 1-by-2-inch hardwood on the seat back support into the seat back. Drive additional screws through the underside of the seat back slats at the bottom into the extra 22-inch cross brace inside the square frame.
Paint or stain your completed slat chair. Once the paint or stain has dried completely, apply at least one coat of clear varnish or polyurethane. If you intend to use your chair outdoors, apply two or more coats to protect the finish from water damage.