I use the grater on my Kitchen Aid mixer to grate the potatoes and onion. Peel, grate, and wrap them in paper towels or cheesecloth and squeeze out the moisture. Heat the oil while you're doing this, just a thin layer on the bottom of the pan. It should be pretty hot but not smoking. If it's not hot enough, the pancakes will absorb too much.
Add the egg in a bowl and mix a bit, then add the potatoes, sprinkle with flour, salt and pepper, and mix up. Drop by large spoonfuls into the oil. They should "sputter" a bit if it's hot enough. Flatten with the back of the spoon or a spatula and let cook about 5 minutes per side. Don't crowd the pan too much.
As they're done, place them on a paper towel in an oven proof dish and place in a warm oven until you're ready to serve. Serve with applesauce, sour cream, or ketchup.