Cut toward the bottom of a cane where the wood is mature. Cut the wood five or six bud nodules long and remove the thin top of the cane. Slant the top cut and cut the bottom straight across.
Paint rooting compound on the bottom cut. Soak the peat in a bucket with water and squeeze out the excess so it is wet but not dripping. Wrap the cutting in the peat and place it in a plastic bag. Store the cutting somewhere cool--ideally a refrigerator, but a cool garage or basement will suffice. Check the cutting every week to make sure it is still moist. Store the cutting until spring.
Remove the cutting from the bag and plant it in a mixture of three parts perlite and one part peat. Place the potted cutting on a heat mat where it will receive adequate heat to callus. (Callus must form on the end of the cutting to produce roots.) Rooting will begin in one to two weeks.
Plant the cutting outdoors in spring after rooting has occurred. Plant the cutting with half of the length in the soil and water weekly. Soak the soil at least 1 inch at each watering (test the depth of moisture with your finger). Water weekly until the cutting has 6 inches of growth.
Fertilize the grape plant weekly with a dilution of fish fertilizer added to water; follow the package instructions for specific dilution rates. Move the vine in fall when it is dormant, if desired, or grow it in its current location if there is enough sunlight and water. Space vines 4 feet apart if you are planting multiple cuttings.