There are a variety of different ways to cook potatoes for potato salad. I just do what my mom does and it works like a charm every time. Quarter potatoes, but don't worry about peeling them until after they've cooked. Start the potatoes in cold water and bring them to a boil to ensure even cooking. This prevents the outside from cooking too fast and the inside taking more time. This is essential for the perfect texture of potato. Salt the boiling water, so the potatoes get plenty of that salty flavor.