Place the potatoes in a large saucepan or pot. Add enough cold water to cover the tops of the potatoes. Add 1/2 to 1 teaspoon salt to the water. Turn the burner on high and bring water to boiling. Reduce heat to medium low or low. Cover the pan with a lid. Cook the potatoes in gently boiling water until tender, about 15 minutes for cubed potatoes and new potatoes and 20 to 25 minutes for quartered potatoes.