The easiest way to dry the shredded potatoes is by wrapping them in a clean cotton tea towel. Gather up all corners of the cloth into a pouch and twist. Spin up the bundle of spuds until liquid begins to wring out of the mass. Alternately, you can spool off a half dozen paper towels and do pretty much the same thing. (I save the wet paper towels, dry them out, and mop up spills with them afterwards.)
Some other critical bits of advice:
NEVER MASH DOWN THE MASS OF FRYING POTATOES!
Doing so will only guarantee you a batch of library paste! Yes, they will sizzle more from being forced into intimate contact with the frying pan, but you will have congealed the entire batch into a massive gooshed bunch of oily crap.
I very loosely pile the washed shreds in a fairly tall heap. Leave about a 1" perimeter around the edge of the pan. Salt liberally before and after turning. If you do not salt them while they cook, once they reach the table no amount of salting will make any difference.
A cast iron pan is one of the few ways to avoid sticking or scorching. I use French Le Creuset pans which are enameled cast iron and they deliver superb results. You must work at a fairly high heat. Low temperatures will tend to steam the interior of the mound and nearly liquify them into paste. DO NOT cover the pan with a lid. That sort of steaming action will provide you with the aforementioned library adhesive.
We are not talking about any kind of diet or low fat dish here. I use a 50/50 combination of butter and oil. Permit the spuds to form a good crust before running the spatula around underneath them. Doing so prematurely will tend to fold raw potatoes beneath the ones that are cooking and make a gooey mess of things.
It is nearly impossible to turn a large multi-person batch using a spatula, without breaking up the crust. For the best results, learn how to flip the entire batch like a restaurant chef turns a pancake. It takes a little practice. You must first release the entire mound of spuds with your spatula. Make sure the batch slides around in the pan freely. The trick to aerial flipping is tossing the entire batch into the air and then quickly dropping the pan below your launch horizon. This will give you the range needed in order to gauge precisely where the somersault will complete. Bring the pan slightly upwards to intercept the potatoes just as they finish their flight rotation. Keep the pan at an angle dropping away from you to avoid any backsplash of hot oil or butter.
BE EXTREMELY CAREFUL OF SPATTERING OIL OR GREASE!
I managed to burn myself quite seriously once due to carelessness. Another trick is to place a pat (or three) of butter on the uncooked side just prior to flipping the spuds. This guarantees that the uncooked side will see a well lubricated pan as it begins to fry. Again, leave the spuds alone as they continue to fry. A nice crust will form and towards the end, tilt the pan at an angle before removing the batch in order to drain it. Gloat secretly to yourself because any diners at your table will be so happy their ears will start clapping!
I top my spuds directly with either soft poached or sunny side up eggs. Those of you who’ve never mashed liquid egg yolk into your hash browns have yet to live. Trust me on this, it is food for the gods.