Prune away much of the grape vine's top growth, leaving only one strong cane. The less growth needing support from the roots, the better the plant will rebound after the transplant.
Dig up the root ball of the vine starting several feet out from the trunk of the vine. You may need to use a backhoe or other large equipment to lift the root ball. Since the roots spread out in the soil, you will be cutting several roots around the perimeter.
Prepare the new site for the grapevines by digging a correspondingly large hole in an area of full sun and good drainage. Set the grape plant in the soil, keeping it at the same level it was before.
Water the area thoroughly to settle the soil in around the roots and to get rid of any air pockets. Keep the soil moist for the first several months until the plant is accustomed to the new site.