Unwind the grapevines from their old arbor, but be careful not to break or damage the stems or foliage. Wear gloves to protect your hands, as grapevines can be thorny. The best time to move grapevines is early winter, when you can combine the move with your yearly pruning session.
Pull the old arbor from the ground and throw it away. Use a shovel to widen and deepen the holes from the arbor to 3 feet deep and 1/2 foot wide. The holes should be spaced at every 2 to 4 feet to provide good support for the grapevines, so dig new holes if you need to.
Place the stakes in your holes and pack soil around them to secure them. Run a length of wire from the first pole in the row to the second, and so on, wrapping the wire once around the top of each stake to secure the line. Tie the wire off and clip it at the last stake in line.
Repeat this process with another "story" 2 feet below the top line. This lower wire must still be 1 to 2 feet off the ground to keep grapes away from disease-bearing soil.
Tie the grapevines up to your new wires, using soft felt or plastic ties. Tie only the main growing stems, with one vine running along each wire away from the canes. Over time the grapevines will train themselves to this new trellis.