I'm no expert, but I did this last year. I successfully grew potatoes using the ones from my CSA that sprouted before I used them.
Â
Some notes for the benefit of others reading this: you don't do this with typical grocery store potatoes, as they are sprayed with a sprout-inhibiter (not to mention a bunch of other stuff, ugh). Also, if you plan to breed potatoes, starting from non certified "seed" is not recommended for reasons I have forgotten. But for someone who just wants to stuff some potatoes under the ground and dig em up later? Good enough.
Â
I cut mine into pieces so there was one sprout per piece. I buried mine as deep as I could, allowing for the length of the sprout. Hill them up as they grow, so they are buried deeper and deeper.
Â
They are very forgiving. I had no idea what I was doing and still got a crop. There were potato beetles that eventually ate the plants to the ground. I still got a crop. I'm sure I could do BETTER if I knew what I was doing, but the point is just that you don't really have to know.