Place a large piece of cardboard on a flat surface. Using a pencil, string and a nail, draw a large arch on the cardboard. The base of the arch needs to be 48 inches wide, so make the section of string from the nail to the pencil 24 inches long.
Use a carpenter's square and a protractor to divide the arch into four equal pieces. Cut the pieces out.
Trace the cardboard pieces on a 2-by-8 board. Trace each piece twice to make two arches. Cut the eight arch pieces out with a jigsaw.
Arrange the eight pieces on the flat working area to create two equally sized arches. Connect the four pieces of each arch using mending plates. Set the arches aside.
Select a level location for the arched arbor. Mark a location for two of the posts 32 inches apart from each other. Mark the location for the second pair of posts 32 inches from each other and 48 inches from the first pair. The post locations should form a rectangle with square corners.
Dig a 2-foot-deep hole at each post location, using a post-hole digger or auger. Keep holes evenly spaced as you dig because the outside edges of the posts need to be placed at the 32- and 48-inch spacing.
Shovel a small amount of gravel into the bottom of each hole. This will help with drainage around the base of the posts to reduce rot problems.
Place a 4-by-4 post in each post hole. Use scrap pieces of lumber to brace the boards together to hold them straight. Use a sprint level to check the straightness of the boards. Make adjustments to the bracing boards as needed.
Cut three 2-by-4 boards each measuring 30 1/2 inches. These boards will be supports for the arch portion of the arbor.
Nail one of the 2-by-4s across a pair of the posts. Nail the board in the center of the top of each post. Repeat with the other pair of posts.
Nail the first arch across the two pairs of posts, attaching it to the ends of the 2-by-4 boards. Repeat on the back of the arbor to install the second arch.
Nail the third 2-by-4 board between the two arches and in the center of both of them. This will hold the arches in place. Remove all bracing boards that were used to install the posts.
Cut many 1-by-3-inch boards 32 inches long; they will be attached between the posts and arches. Use a scrap piece of 1-by-3 lumber as a spacing board to help keep the boards an equal distance apart. Screw a board across the first pair of posts 6 inches up from the ground. Continue installing the boards until you reach the top of the posts. Repeat with the other pair of posts.
Install 1-by-3s across the two arches in the same manner as the previous step. Use two screws at each meeting space.
Pack the dirt from the post holes back into the holes around the posts. Tamp the ground around the arch to pack it very firmly in place.