Sweet potatoes have to be one of the more fun kitchen-food plants to grow in the home. The best ones to grow are organic ones that I get at the farmers market, since the local farmers, at least who sell in NYC,often don't spray anything on the potatoes to prevent sprouting. The ones I get at the supermarket never seem to ever give off any slips!
If you don't get around to eating your sweet potato and would like to try your hand at growing one in the home, then I encourage you to do it. Surprisingly, one sweet potato can produce up to 50 slips, or so I read. These "slips" are simply sprouts that come off of the tuber. You don't need to put the tuber in water for it to grow slips, but when you start to see the sprouts emerge, I'd place the potato in a jar of water.
Toothpicks can be used to hold the potato in place so it doesn't fall completely in the water. All you want is about 1/3 of the sweet potato submerged. Place it on a windowsill and replace water every other day or every third day. If you don't, the water will get pretty scummy.
In a few weeks, the leaves will start to appear and unfurl and the roots of the potato will look like the below. You may want to move your potato to a larger jar for a little while longer, or you can start to twist off some of the slips, place them in a shallower jar of water and wait for a few days for the roots to fully develop. Once that happens, you can begin to transplant some of the slips (provided they have a substantial enough root system) into a large pot with loose, well-draining potting soil. I typically plant mine in the largest pot I can find. After all, these are underground dwellers and you want to get as big of potatoes as you possibly can.
