We just take a regular sweet potato root (we've used them right from the grocer when we didn't have any of our own to get started) and put a couple toothpicks on each side, placing it in a small (yogurt size) container w/ water filled about half way up the root.
Place containers in a warm sunny location, changing water daily, we put ours under a fluorescent light in a window bay that also gets alot of sun 'when' it shines :).
After the 'mother' root begins rooting in the water, you'll see sprouts forming from the portion above the water line. Let these sprouts develop to 2-3" (at least three leaves) and then 'rub' them off right at the base of the 'mother' root and place these 'rubs' in some 'shallow' water (1/2 -1") and w/in a few days you have 'seedlings' ready to put in a 4-6" pot until your particular garden climate can accept them.
We have an unheated greenhouse that we'll transfer the plants to as they grow and temps get warmer, and up here at least we don't put them out in the garden until after Fathers Day.
This probably seems more complicated than it is and for that I apologize :-\ It really is a simple process and "well worth the effort" IMO.
I mean really :?. How else could we cultivate these wonderful beauty's in North Wisconsin any other way 8-)