Question: I came across a recipe for skillet potatoes that asked for "cooked potatoes cut into 1/4-inch chunks". While the 1/4-inch chunk part was easy to understand, I'm not sure what is meant by "cooked". Boiled? Sauteed? Baked?

Answer: 
The best way to pre cook potatoes is to do a rough chop and cook in boiling salted water until fork tender, not mushy. A 1/4 inch dice is way too small to do that.

Try dicing the potatoes into 1/4 inch pieces, place in a pile wrapped in wet paper towels into a micro safe bowl and microwave for 3 minutes, add time and more dampness if not done yet.
If you have enough time for preparation, just put the potatoes into the pot without peeling them, bring them to a boil and leave for an hour or so. If they are still hard when you prick them with a fork or knife, bring them to a boil once more. this way you can get them cooked gently without much energy expenditure. Cooking them in the skin also preserves more of the nutrients which sit under the skin.