First you want the right potatoes, a medium starch content works best. Waxy potatoes don't work, they have too much water in them. Maris Piper potatoes work well, in the US Yukon Golds are a good choice.
Next you have to peel them, don't try and get them crispy with the skins on. Crispy skins are great, but you'd use a different method then this to get them.
Boil them in salted water until you can get a fork into them but they aren't completely done. Drain them while still in the pot and then shake them around a bit as it will rough up the outsides, giving a good surface area. This is the real secret, the rough outside of the potatoes.
While the water was heating up you needed to be putting a baking tray in the hottest oven you can manage or just below the smoke point of your oil or fat. Do not use olive oil, butter or anything with a low smoke point. Goose fat, duck fat, peanut oil, canola, sunflower will all work, it all depends on how thick you want your arteries to get ;) . 200C (about 400F) is a good temperature to shoot for with most oils.
Once the potatoes are boiled, drained and roughed up get the hot pan with the oil out and pour the potatoes in, spreading them out. Tilt the pan so the oil pool at one end and use a big spoon to coat the potatoes in the oil, then get them right into the oven. Really crispy potatoes take about 45 minutes, it helps if you take the pan out halfway and turn the potatoes over, then do the tilt and spoon trick again. Once they're done get them out of the oil into a bowl, you don't want them sitting in the oil when you serve.
If you overboil the potatoes you can come back from it, you simply shape the loose potato with your hands and drop them onto the pan, the outside will harden and get crispy, holding it all together. I know people who boil their potatoes until they fall apart on purpose as they like them that way, to me it's too much extra work, but they do get really crispy.