We grew potatoes one year. We'd never grown them before, but at my grandma’s urging, accompanied by her recollection of her family growing them in a "truck patch," we decided to plant them. Now this was back when we knew next to nothing about gardening, so we did it just like we were told. (That way we could blame Grandma if things didn’t work out.)
We cut the potatoes into pieces with two or three eyes on each piece and let them dry out for a couple of days. Then we made “hills” in the garden, about 18 inches apart. In each hill, we put three of the pieces of potatoes about six inches apart and four inches deep, then covered them with soil. That’s all we did, and mid-summer, about two weeks after the plants began to die back, we dug up potatoes!
This year, we’re growing them in a new way (for us). We got discarded black plastic 55-gallon barrels from Romie’s place of employment and cut the bottoms out of them. We placed topsoil in at a depth of about 8-10 inches, layering it with compost, then placed four sections of seed potatoes on top and covered them with soil about four inches deep.