Larry - I start them in something real loose - even sand. The slips pull easier. Put a few inches of loose soil, sand, or compost in a container. Lay the potatoes on top, as close together as they'll fit, then cover them up with more loose soil. I set them in the sun, with a piece of glass over the container to generate warmth. Gotta keep them moist. Also - I have a compost pile in a cage made of hog panels. Last year I set some right in one corner of the compost pile, and used an old storm window for heat and protection. If it's calling for frost, I lay a folded tarp over the whole thing. I knew an old guy who cut his potatoes in half lengthways and set them in loose soil. Said they produced more slips. Never tried that, but might this spring. I use potatoes from the previous year to start the slips, and I seem to have better luck with the culls - potatoes an inch or so in diameter.
"Once you plant, do you include a small piece of the potato with the slip attached?"
No - you don't plant any part of the potato, only the slip that's pulled off of the "mother".
When I plant them, I first throw up a nice ridge, then I take a sharpened piece of a broken shovel handle to make as deep a hole as I can in the ridge. 12" spacing in the ridges. I stick the slip in the hole until there's only the top two leaves showing, then I water it good before I cover it up, leaving a nice big cup in the dirt to help with future watering. When you pull the slips, keep them wet until you plant them. If you can get them in the ground quick, you'll not have many die.
Experiment a little and see what works best for you.
I gave away over 500 slips last spring. I usually start them the first of April, for planting the first of June here in Southern Illinois.
Sorry for the long post.