Put potatoes in a pot. Add enough water to cover the potatoes by an inch. Salt the water until it tastes like the sea. Place over high heat. Bring to boil. Turn down to the barest of simmers.
Now here is the real trick - do not under any circumstances allow the water to boil. Doing so will cause the potatoes to crack, absorb too much water and break apart.
Cook for about 20 to 30 minutes until the potatoes are tender when pierced with a fork. Remove potatoes from water. If you are going to mash them, do so while they are still very hot. If not using immediately, cover and refrigerate.