I've made some progress but I'm still not satisfied with the results. I think I figured out the secret of having them not stick to the pan. You need to preheat the pan on medium-low with a little oil in it. After you add the potatoes, don't try to stir them right away. Let them brown on the bottom for a minute then you can flip them over.
But so far, even when I can get the outside the right golden-brown color, my hash browns are coming out kind of dense, soggy, and gray on the inside, not light and fluffy like at the cafe. What am I missing? Do I have to peel them before I grate them?