Prepare the soil a year before planting the Concord grapevines. Locate a well-draining site in your garden with full sunlight and a pH level between 5.5 and 6.5. Till the soil to a depth of 10 to 12 inches, removing exposed debris, stones and weeds. Two to three weeks before spring planting, add a standard fertilizer to the soil and mix well.
Dig a hole in the planting site as deep as the grapevine's root ball and two times as wide. Set the plant at the same height it sat in its previous container before covering its roots with soil. Tamp the soil around the plant to firm it. Prune the tops of the plant to a single healthy cane or two to three buds to force it to produce new growth. Space multiple plants 6 to 8 feet apart in a row, with rows spaced 9 feet apart.
Water the Concord grapevine one to two times every week, providing it 1 inch of water at every session. Feed the grapes a high-nitrogen (10-6-4) fertilizer two weeks after planting, at the rate of 10 lbs. per 100 feet or row space. Alternatively, feed a single plant 1 lb. of fertilizer.
Insert a 5-foot-long stake into the ground, 3 to 5 inches from each grape plant. Train the strongest cane on the plant to climb the stake using elastic ties. Remove suckers from the base of the canes with sharp scissors.
Construct a trellis to support growing vines. Insert two 7-foot posts 12 inches in the ground. Space the posts 8 feet from each other. Extend two lengths of high-tensile between the posts, one spaced 3 feet above the ground and the other spaced 5 feet from the ground.
Attach the growing Concord grapevine to the horizontal wires when it reaches the top of the stake. Cut growing branches along the main trunk down to two buds along the lower wire to encourage the plant to grow and spread its canes horizontally.
Pull out any weeds that grow near the Concord grapevine and compete with it for soil moisture and nutrients. Spread a 3-inch-thick layer of organic mulch around the plant to reduce weeds and keep roots cool.