Use a table saw with a miter fence to cut the ends of all lumber to 90 degree angles. This ensures that all your boards will be cut to the correct angles and that you will be able to plumb and level the swing as it is being constructed.
Cut a 7-foot long top rail for your swing frame from 2-inch by 4-inch stock lumber. Use 2-inch by 3-inch metal brace plates to attach a 4-inch by 4-inch by 10 foot long post to each end, as shown in the diagram that accompanies this step. Secure with 1/2-inch diameter, 1 1/2-inch long galvanized wood screws.
Use a hand auger to dig two holes whose center points are 6 feet 8 inches apart, 2 feet deep. Have a helper assist you in raising the swing frame up and putting the posts into each hole. Fill empty space around each post with flat-sided gravel, half the depth of the holes.
Use a plumb bob hung from a spirit level resting on the top rail to check for plumb (straightness up and down) and level. The bubble of the spirit level will be between the two lines if the frame is level, and the frame will align with the plumb line if it is 90 degrees in relation to the ground. Brace the swing frame to hold it in position.
Mix quick-set concrete in a wheelbarrow according to package directions. Fill each post hole with concrete. Allow to set overnight and up to five days, depending on the humidity.
Cut two bench back braces from 1-inch by 2-inch stock lumber as shown in the diagram that accompanies this step. The back pieces should be 2 inches by 1 inch by 24 inches. Miter them from 2 inches wide at a point two inches from one end, down to one in wide at the other end. Cut three seat bottom pieces 18 inches long by 2 inches by 1-inch.
Cut two 5 feet, 10-inch long front and back frame pieces from 1-inch by 2-inch stock lumber. Place between two of the back braces and secure using 1/4-inch diameter, 2-inch long galvanized wood screws.
Cut 1/2-inch by 2-inch stock lumber to fit across the swing back and seat. Secure with 1/4-inch diameter, 3/4-inch long galvanized wood screws. Place the pieces 1/2 inch apart across the seat and back until it is covered as shown in the diagram.
Attach two eye hooks at each end of the bench in the positions shown in the diagram. Attach the coated chain to one eye hook using open S hooks. Pass it through the galvanized ductile iron swing hangers and back down to the second eye hook. Use vise grips to pinch the S hooks shut.