Place a 75-inch plank of 1-by-2 lumber 2 inches down from one edge of a 75-inch 2-by-12. Secure the 1-by-2 with 1-1/2-inch screws driven in every 5 inches along the length. Repeat with a second 2-by-12 and 1-by-2. These are the side rails of the bed frame, with the 1-by-2 planks as the slat supports.
Stand the side rails up with the slat supports facing inward and closer to the top edge; move them 40 inches apart. Insert two 40-inch 2-by-12 planks between the ends of the side rails, making a rectangular frame. Attach the 40-inch planks with four evenly spaced 2-1/2-inch screws through the side rails into each end of the 40-inch planks.
Insert a 72-inch piece of 2-by-10 lumber in the center of the frame, parallel with the side rails. The top of the 2-by-10 plank should be flush with the top of the slat supports. Secure this central support plank with four evenly spaced 2-1/2-inch screws through the end planks into the ends of the support plank.
Turn the frame over, so that the slat supports are closest to the ground. Insert a 15-inch 4-by-4 into each corner of the frame for the bed legs, keeping what will be the top end of the legs even with the top of the slat supports.
Attach the legs with four 2-1/2-inch screws through the side rails of the frame into the legs, and four screws through the end rails into the legs. There should be eight screws securing each leg.
Turn the frame back over so that it is standing on the legs. Insert 30 slats that measure 1/2-by-2-by-40 inches across the bed frame, parallel with the ends and spaced about 1/2 inch apart. Secure the slats with 1-inch screws through the slats into the slat support and central support -- three screws per slat.