Take 12 to 18 inch cuttings from an established grapevine plant in early spring, making a slanted cut at the top and a flat cut at the bottom for identification. The cutting should have at least 3 or 4 nodes, which are the swellings in the vine where the leaves attach.
Take a pot with drainage holes and fill it with potting soil. The grapevines are not partial to any particular type of soil. Plant the cuttings in the soil with the flat end down, leaving one node above the soil. Keep the soil moist throughout the first year of growth so that the roots can establish themselves. After that, the soil can dry slightly between waterings.
Place the pot in full sun, in either a window or outside if the frost dates have passed. This is the only demanding requirement of the grapevines.
Provide a trellis support for the plant as it begins to grow. Train the vine up the trellis as it grows so it can support itself if it produces fruit.
Prune the vine in the first winter after its first full year. Choose the strongest shoot and cut back all others to the ground. In subsequent seasons, prune only to maintain the vines.