Place a 10- to 20-gallon container in a warm area where it can get as much sun as possible. If the container doesn't drain well, use a hammer and nail to poke additional drainage holes in the bottom. Fill the container with sandy potting soil. Take the temperature of the soil occasionally to ensure the soil temperature remains between 70 and 90 degrees Fahrenheit.
Transplant one or two new slips into the container, leaving at least 12 inches of space between them. Cover the roots with 1 to 2 inches of the sandy soil.
Water the slips well, and ensure that excess water drains from the container. Sweet potatoes should have moist, but not overly wet, soil. Water as the soil dries out, and reduce water levels as the plants mature and approach harvest time.
Cover the container loosely with black plastic film, if necessary, to help the soil maintain heat.
Add an additional inch or two of soil when shoots appear.
Support the vines with a trellis or other supports stuck into the container, behind the vines. You can secure the vines to supports with loosely tied lengths of twine. Harvest the sweet potatoes carefully, using a large spoon rather than a spade, to dig around the roots. This prevents accidentally bruising or tearing roots when you are looking for the sweet potatoes.