Take cuttings of the current season's growth from partially mature wood. The best time to take cuttings from grapevines is mid-July through early autumn. The wood should be relatively firm and the leaves at their mature size. Make each cutting 6 to 8 inches long. If possible, take the cuttings in early morning, as the plants are fully hydrated then and the cuttings have less of a chance of drying out. Protect them in a plastic bag until ready to proceed.
Fill a shallow pan with a soilless mix such as peat moss or vermiculite. Set the shallow pan into a larger pan. Add water to the larger pan until it is half way up the sides of the smaller pan. Allow the smaller pan to sit in the water until the surface of the growing medium is damp. Remove it from the larger pan and allow any excess water to drain away.
Remove the leaves from the lower 1/2 to 1/3 of the cutting.
Push the cuttings into the vermiculite, burying 1 to 2 inches of their stems in the soilless mix. Space them 1 to 2 inches apart in all directions. Firm the growing mix around the base of the cutting so it stands up on its own.
Place the pan of cuttings into a large, clear, plastic bag. Leave the bag unsealed so air can circulate. The plastic will help keep the cuttings from drying out, while the unsealed top will help keep mold from forming on the cuttings.
Set the pan of cuttings in the shade. Check them regularly and water as needed to keep the growing medium evenly moist.
Check the cuttings for roots about six weeks after making the cuttings. Gently pull on one of the cuttings. If it resists coming out of the growing medium when you gently pull on it, roots have formed and they are ready to transplant into a nursery bed until the following growing season.