I've found some info about growing sweet potatoes for you, and I think I might even give it a go myself!
Bury the mature sweet potato halfway into moist potting soil and keep the soil moist. Or put enough toothpicks in the midsection of the sweet potatoes to hold the potato up in a jar of water. Cut the slips off the mother sweet potato when they are six to eight inches long. Remember to handle the slips gently at this point because they are easy to damage. Transplant the slips in the garden when there is no danger of frost. Lay the slips on their sides with most of the slip buried a half inch under the soil. Plant the slips 12 to 18 inches apart in rows that are three to four feet apart. Sweet potato vines will cover the ground; therefore, they need a lot of space in the garden. Place black mulch around the young sweet potato slips to help retain moisture. Black mulch will also draw heat from the sun. Harvest sweet potatoes before the first frost. Sweet potatoes are ready to be harvested after four months in the ground, no later than five months. Dry the sweet potatoes on the ground two or three hours after harvesting. Then allow them another 10 to 14 days of curing in a warm room with moderate humidity. Afterwards, they should be placed in a cool room for storage until ready to be cooked.