Dig two holes with a post-hole digger to a depth of at least 3 feet. Position the holes 10 to 12 feet apart, with the Concord grape positioned in the center, equidistant from the holes. Use a retractable metal tape measure throughout this project. "Sunset Western Garden Book" states the holes can be as far as 15 to 20 apart, especially if the Concord grape is well-established, large and your climate typically allows the plant to grow to large proportions each summer and fall after its annual early spring pruning.
Insert an 8-foot wooden post into each hole so that at least 5 feet of the post remains above the ground. Backfill the holes if needed to get 5 feet of wood length above the soil.
Pour quick-setting concrete into the hole around the wooden post and allow it to harden sufficiently. Consult the product bag for specific recommendations based on ambient temperature and your soil type. Alternatively, mix concrete from sand and cement in a wheelbarrow to anchor the wooden posts, but this takes considerable more time to complete and cure.
Insert heavy-duty eye screws into the wooden posts to create the basic foundation for the wire trellis system. Place the bottom eye screw 2 1/2 feet high from the ground each post, and the second eye 4 1/2 to 5 feet high, according to general recommendations listed in "Sunset Western Garden Book."
Wait until the concrete bases on the wooden posts has cured and hardened well before installing the wire cross-lengths. Cut two 15-foot-long pieces of heavy-gauge wire with a wire cutters. Insert 18 inches of one end of the wire piece into the lower eye screw on one post and twist and wrap it around the wire to create a snug, tight attachment. Pull the other end of the 15-foot wire piece into the lower eye-screw on the other post. Pull it taut and then bend and twist the wire end around the wire to attach it securely. The wire should be sturdy and snug when you place your hand in the middle of the wire between the pole, sagging little or not at all.
Attach the second 15-foot-long piece of wire in similar fashion to the posts' upper eye screws.
Lift up the vines of the Concord grape in the middle of the posts under the double-wire trellis and assign each vine a spreading, horizontal position on the trellis. Tie the vine to the wire with garden twine. Make the tie snug, but allow room for the vine to will expand--you don't want to constrict the expansion of the vine's diameter. Feel free to gently wrap the grape vine as needed around the wire trellis to provide sound support.