Once the posts have been set, the rest of the structure can be built in a half day. Widely spaced 1x3 braces allow room for robust plants to climb, but are far enough apart to discourage small children from using the trellis as a jungle gym.
Choose wood that will last in your climate. If you plan to paint the structure, pressure-treated lumber is an affordable choice. 1x3s are needed for side braces. If your lumberyard does not have 1x3s, they should be able to rip 1x6s to size for a modest cutting fee. In addition to basic carpentry tools, you will need a posthole-digger, a shovel, and something in which to mix concrete -- a deep wheelbarrow or plastic mortar box. Rent a power miter saw if you are not confident about making accurate 45-degree cuts on the 2x4 rafters. With a posthole digger, excavate postholes that extend below the frost line or at least 24 inches deep. Pour in 2 to 3 inches of gravel. This keeps the bottom of your posts from direct contact with the soil.
1. Prefabricate the framing by fastening the notched top plate to the posts using 3-inch screws. Add two temporary cross braces so you can set the whole section into the postholes at once. Set the section in the holes, check that it is plumb and level, and attach the temporary braces as shown. Pour the concrete and trowel it so it slants away from the post, just above grade. (This keeps water from gathering at the base of the post.)
2. Build frame. Add the other 2x4 top plates to join both sections, fastening them with 3-inch deck screws. Cut 2x4 rafters so that the longest side of each measures 36 inches. Make 45-degree cuts at both ends. Join the upper ends of the rafters with angled 3-inch deck screws. Set the piece in place to check that the fit is right. Adjust as needed and fasten with 3-inch screws. Use 1-5/8-inch screws to attach the sidepieces to the 4x4 posts, maintaining equal spacing between the pieces.