First, stick 3-4 toothpicks around the center of the sweet potato.
Place it in the glass. the toothpicks should rest of the end of the glass holding the sweet potato up so it is not touching the bottom of the glass.
Fill your glass up with water so about 1/3 to 1/4 of the sweet potato is submerged in the water.
Anywhere from a few days to a week or two you should start to see roots sprout from the submerged part of the sweet potato.
After a while longer, you should see stems (and if you leave it long enough, leaves sprouting out of the top.)
Keep it in a warm sunny window and keep adding water as needed.
Once you have a good amount of white roots established, you can leave it in a container of water or plant your potato in some soil. Sweet potatoes do well in all types of soil.