Sweet potatoes aren't started by seed like most other vegetables, they're started from slips. Slips are shoots that are grown from a mature sweet potato. Each sweet potato can produce up to 50 slip sprouts. To create sprouts, carefully wash your potato and place it in a jar half submerged with water. Hold it in place using toothpicks. Some tutorials I read said to cut the bottom portion off. I am not sure if this just makes the roots grow faster? I didn't do it, but you can. The slips need warmth, so put them on a window.
Once all of the slips are in place water them. You'll need to give them a thorough soaking until all of the surrounding dirt is wet. Stop watering before your mound starts to erode. New plants, like slips, need to be watered everyday for the first week and every other day the second week. Each week the watering will get a little farther apart until you're watering once a week. If the ground is very dry or you've had a lot of rain, you may need to adjust this schedule in your own garden. Sweet potatoes can withstand drought but they'll produce less, so make sure you water them during the hottest part of the summer." The roots mature and are ready for harvest by late September and early October. This gives them time to harvest before the first frost, so the potatoes are in storage as the weather turns cool. For tips on harvesting, and curing for long term storage- See here.