If you are talking about boiling potatoes for mashed potatoes, 20-30 mins. After 20 minutes stick a fork on them if it goes on easily they are done. Also the smaller you cut them up the faster they cook.
The trick is to soak them before you cook them. Get the starch out of them by placing them in water. If you are going to boil them in water, say for mashed add a pinch of salt to the hot water a quarter them. Boil until you can cut with a fork. Then mash. Add milk and butter. To fry repeat the soak then pat dry. I use peanut oil. get the oil hot, then add a little at a time. cook until they turn brown. For hash browns use a cheese greater. then soak, pat dry then add an egg, mix and place on dry frying pan. A hand full will do then add oil on top of hash browns. Med heat. Don't peak. Let them cook for 3 to 5 min then flip. They will come out crispy.