Although grapevines can be started from nursery stock, if you have access to an existing grapevine, you can easily root a plant from a cutting. There are several types of grapevines, so determine the final purpose before you begin. If you want to make jams and jellies, keep in mind that you need a different type of grapevine than that grown for wine. Whatever type of vine you choose, you'll have a lovely vine fairly soon, and fruit in a few short years.
Collect cuttings from a dormant grapevine in early spring, as soon as the weather has warmed and there is no danger of frost. Locate a few plump, healthy stems and with sharp, sterilized garden shears, cut lengths of vine with at least four nodes. Nodes are the points on the vine where a tiny bud is beginning to develop. Keep track of which end of the cutting is the bottom node, or the node that was furthest from the soil.
Put the grapevine cuttings in a bucket of water immediately. Let them sit in the water for at least 6 hours but no longer than 24 hours.
Choose a sunny, well-drained spot to root the grapevine and loosen the soil in an 8 foot circumference so the roots will be able to spread easily. Keep in mind that grapevines can grow in rocky soil where most plants won't, as long as there is excellent drainage. Don't plant the grapevine where the roots will sit in water.
Dig a hole large enough to accommodate the grapevine. Dip the bottom of the root in rooting hormone solution and plant the vine with three bottom nodes in the soil and the top node above the ground.
Let a garden hose trickle into the hole while you refill the hole with dirt, and let it run until the cutting is soaked. Water the grapevine often for the first month.
Start training the grapevine on a trellis as soon as it's a few inches tall. Adjust the vine often to make sure it's headed the right direction. Once the vine is established, it won't need to be adjusted as often.