I've grown sweet potatoes in the garden for a few years but didn't try to start my own slips until last year. A friend's grandpa grew the biggest sweet potatoes--football size sometimes-- and I tried to start slips according to his method.
He said to take a big black bucket, like a feed bucket, and put fresh manure in the bottom of it. Cover the manure with soil then place the sweet potatoes on the soil, cover with soil, then cover with hay. In a few weeks sprouts are supposed to start coming out. All I could get out of this method was rotten potatoes.
While "googling" how to start sweet potato slips I ran across many folks who just sprouted them like you would an avocado pit. Cut the sweet potato in half then suspend it with toothpicks in a glass with water. Put the cut side down and set the glass in a warm spot in the house. I put mine all around the woodstove in the livingroom.
It took a few weeks for them to start sprouting, but sprout they did! I've got around 30 glasses with sprouting potatoes in them. When the sprouts get about 6" long pull them loose from the potato and place in a glass of water. If the sprouts get too long before time to plant you can take cuttings from them and stick the cuttings in the water to root. I've got one jar with about 40 sprouts I've pulled off the "mother" taters, and I check them daily for new sprouts that are ready to be on their own. One of the CSA members came to visit a few weeks ago and she laughed and said that reminded her of her classroom years ago when she would have the kids sprout things and plant seeds just to teach them where food really comes from.
See......most of what we really needed to know we probably did learn in kindergarten!