Germinating grapes from seed is a task reserved for gardeners who are looking for a challenge. The success rate isn't promising, because only a small percentage of seeds will ever germinate, and if they do, they won't be ready to bear fruit for about 3 years. In addition, the genetic make-up of the original seed won't be passed to the new plants, so the grapes might look and taste very different. It's easier to purchase stock from a greenhouse or nursery, but germinating grape seeds can be an interesting experiment, and successful attempts are a major accomplishment.
Save the seeds from several seeded grapes. Soak the seeds in a bowl of warm water overnight, then skim off and discard any seeds that float to the top.
Put about a cup of organic material such as damp perlite or peat moss in a plastic bag and push the grape seeds into the middle of the bag. Be sure the organic material is just damp, but not soaking wet.
Place the baggie in the refrigerator and leave it for at least three months. Check occasionally to be sure the organic material is still damp. This process, called stratification, replicates the natural conditions in nature, where the seeds will fall on the ground and will winter over before they are ready to germinate in the spring.
Fill some 2-inch planting pots with commercial potting soil or peat pots. Remove the grape seeds from the refrigerator and plant 2 or 3 seeds in each pot. The seeds should be kept at about 72 degrees during the daylight hours. If the room is too cool, put the pots on a heating pad or under a heat lamp to keep them warm. Watch for the seeds to germinate in a few weeks. Keep the soil evenly moist with a spray mister.
Transplant the grape seedlings into larger pots when they're about 2 inches tall. Leave the seedlings indoors for at least a year before attempting to move them outside.