Propagating Sweet Potato Plants
Although these plants are the same species as the sweet potatoes we grow for food the ornamental sweet potatoes have been bred for ornamental characteristics, not culinary uses. As an alternative to eating them, you really wouldn't like their taste, you can try over-wintering them for replanting the next year. Dig them up in the fall after the first hard frost and store them in a cool location with some slightly damp peat moss. As long as they don't dry out you can replant them in the spring. Some cultivars like the Margarita may develop large sweet potatoes while other cultivars will produce small sweet potatoes and some may not produce any at all. 
New plants can be easily propagated from slips (stem cuttings). Slips are sections of a sweet potato vine that is used for propagation. A slip or cutting from a sweet potato vine should be approximately 6 inches long and contain at least 2 leaf nodes (bumps in the stem where leaves develop). Make your cut below the lowest leaf node and remove lower leaves on the cutting leaving a few at the top of the cutting. Place your cutting in a pot filled with a well-draining potting soil and keep soil moist. Cuttings can also be placed in a glass of water as cuttings will easily roots without soil or rooting hormones. I like to put my cuttings in water as it is easier to see the root growth. Make sure one or two of the leaf nodes are covered by soil or water as the new roots will develop at these leaf nodes. Take care to keep soil moist or water in the glass at a level above the leaf nodes. In a week or two enough roots will have developed allowing the cutting to be planted in the garden or in a container.
Below is a link to a container garden design using an ornamental sweet potato cultivar and a link to several sweet potato plant files. The plant files will help in explaining the different cultivar characteristics such as leaf shape and color.
http://www.gardenality.com/Search/#Tab=Plants&PageIndex=1&PageSize=10&PlantSearch=null&SortBy=undefined&SearchText=sweet potato&Attributes=null
