Select a pot 24 inches or larger that isn't black plastic, which will retain heat and make the roots too warm. Plant in terra cotta pots as a good choice, but they require more frequent watering.
Plant a self-pollinating grapevine, such as "Delight," that is recommended for container growing.
Place a layer of large stones or broken terra cotta potsherds in the bottom of the pot to aid drainage. Fill the pot with potting soil.
Make a hole in the center of the pot. Plant the grapevine so that all roots are covered. Water until water runs out the bottom of the pot. Keep the soil evenly moist during the first growing season. Let the soil dry out between watering thereafter.
Place a trellis in the pot. Loosely tie the vine to a trellis with soft cord or sections of old pantyhose.
Place the grapevine in a sunny location.
Fertilize three to five times during the growing season with a low nitrogen fertilizer, such as fish emulsion. Follow the label instructions for dosage.