The potato can be grated by hand like cheese or shredded in an appropriate blender. The onion can be roughly chopped by hand or in a blender but try to avoid large chunks as much as possible as these will affect the flavour and the way in which the hash browns hold together.
Place the shredded potato in a sieve or fine colander and press down with kitchen paper to remove as much moisture as possible.
Ensure the onion is well broken up and not layered, then add all of it, plus all of the dried shredded potato to a medium sized bowl and combine well.
Lightly whisk the egg then add to the potato and onion mixture.
Add the salt and pepper - amounts are an estimate and depend on personal taste, but seasoning is essential. Other flavourings such as cheese, chilli, spices or herbs can be added here.
Heat the oil in a frying pan. Note: the oil MUST be hot so that the hash brown begins to cook as soon as it hits the pan. Otherwise it will absorb the oil and the flavour and crispness will be affected.
Take about a 1/4 cup of mixture and drop carefully into the pan, flattening immediately with the back of a fish slice (commonly mistaken for a spatula, so if you don't think you have a fish slice use what you think is your spatula). If you're not sure what a 1/4 cup is, divide the mixture into 4 and you're about right.
Cook each side for 2-3 minutes. Slide the fish slice under slowly when intending to flip it over just to check it has been cooked long enough on that side. If it hasn't, it won't hold enough to allow itself to be flipped.
Hash browns keep well in a warm (but off) oven so if you're planning them as part of a fry-up breakfast I'd recommend doing them first and keeping them in a warm oven while you cook everything else.