Gather scion wood from healthy Concord grape vines in January or February. Select canes that previously grew in full sun with healthy buds that have not suffered freeze damage. Use canes that are about 1/4 inch to 1/2 inch in diameter. Allow two buds per graft and two grafts per trunk. Place the cut ends of the scions in moist toweling until you are ready to graft each piece.
Cut the trunk of the existing vine you will use as root stock to the desired height for the placement of the grafts using a pruning saw or loppers. Clean up debris to prevent spreading diseases.
Use a pruning saw to make two small cuts through the bark and slightly into the cambium layer near the base of the trunk, one cut on each side of the trunk. Make the cuts about 1/4 inch deep. The trunk will "bleed" sap through the cuts. Make the cuts before you graft or the sap flow will dislodge the grafts.
Cut the scion canes into sections with hand pruning shears. Each section should have two viable buds. Keep the scion sections moist in wet toweling.
Make a 30 degree diagonal face cut on the trunk by beginning about 2 inches from the top of the prepared trunk and drawing the knife up to the cut top edge. The face cut should expose the cambium layer with the bark removed. Prepare the grafting face further by making two incisions about 1 inch long downward into the cambium of the face cut. Prepare a face cut on the opposite side of the trunk for the second graft.
Make a long diagonal face cut on the bottom end of the scion that matches the length of the face cut on the trunk. Turn the scion over and make a steeply angled cut across the tip of the first scion cut to create a flat point. Beginning in the center of the scion face cut, make an incision about 1 inch long to "split" the scion face cut. Repeat with another scion for the second graft.
Hold a prepared scion so the face cut meets the face cut of the trunk. Open the slit incisions of the trunk and the scion slightly, and slide the scion section into place with the outer bark of the scion exposed and the inner cambium layers of the scion and the trunk interleaved. Repeat with the scion of the second graft.
Wrap grafting tape around the trunk to secure the scions. Paint grafting sealant over all wounds. Paint over the grafting tape.