Look for a location in your backyard that provides the distance you need between the place you shoot from and the backstop. The distance from your shooting location to the backstop should range from 20 to 40 yards. Closer distances are best used for precision shooting. Measure the distance with a tape measure, using a stake marker to temporarily identify each 20-foot section.
Measure the chosen spot in the backyard for the backstop at two points across from each other 1 to 2 inches shorter than the length of the two-by-four in your materials. Mark each end on the ground with outdoor marking paint.
Insert the post-hole digger into the ground at the first marked location. Dig down no more than 2 feet, but not less than 1. Repeat for the other end of the marked location.
Insert one round fence post into the first hole. Tamp down dry fence post concrete around the base of the pole, as a helper holds it straight. Periodically check its straightness with the level. Repeat for the other side, using one small bag of fence post concrete for each post. Spray a bit of water over the fence post concrete, but don't thoroughly saturate it. The concrete also draws moisture from the ground, which causes it to harden. Let the concrete harden a day or two before continuing. Cover the concrete with a mound of dirt.
Set the two-by-four on its widest side perpendicular to the posts. Align it with the tops of the posts against them flat in front. Hammer the two-by-four into place with the nails after the concrete is hardened and the poles don't move.
Attach one oriented strand board to the bottom section of the backdrop between the two posts, aligning it with the top two-by-four. Secure the OSB board or plywood to the posts with the 2 1/2-inch nails. Measure and cut the second piece and secure it in place above the first. This serves to stop the arrows from going through the carpet.
Align the carpet remnant so that its longest side aligns with the top of the horizontal two-by-four. Attach it to the OSB boards by nailing it into place along the perimeter, spaced at every foot, with the short-shank flat-head nails.
Set your target in front of the backstop or hang it centered between the two posts.