You cook sweet potatoes by boiling peeled, cubed chunks in a large pot of salted water for about fifteen to twenty minutes until fork tender. Start by placing the cut pieces into cold water, bringing it to a gentle boil over medium high heat, and then simmering steadily. Whole unpeeled sweet potatoes take slightly longer, usually requiring twenty five to thirty five minutes of boiling depending on their thickness. Drain the cooked potatoes thoroughly before mashing or serving them.