Sweet potatoes aren't started by seed like most other types of vegetables, they're started from slips. And slips are shoots that grow from mature sweet potatoes.
To start rooting the slips, you'll need several healthy sweet potatoes.
To create sprouts, wash and cut the sweet potatoes in half. Place each part in jar of water with half of the sweet potato below the water line. You can use toothpicks the sweet potato in place.
The sweet potato slips need warmth, so put them on a window that get a lot of sunlight or on top of a radiator. Keep adding water as needed.
In a few weeks your sweet potato slips will be covered with leafy sprouts on top and roots on the bottom.
Once you the slips have a good amount of roots, you can plant them in your garden.