Peel 3 or 4 or 5 nice big mealy potatoes, like Russets. Grate them quite finely into cold water. Put a tea towel in a colander and pour the potato/water combo in, then press the water out, ending by wringing the potatoes in the towel.
Put the potatoes in a bowl, and add some grated or finely chopped onion, like one large onion, 2 eggs, and maybe a half cup of flour or more, salt and pepper. You can use Matzoh meal instead of flour, I hear, although I never have.
Then, heat a frying pan up and put oil or butter in. I don't know what the Jewish rules are here, I do things the irreligious way!
Put quite a bit in, not just a dab, not just enough to make the pan shiny. Let it get quite hot, but not yet smoking. I actually use butter and oil both, the oil raises the smoking point.Drop three or four NO MORE gobs of potato mixture in, each gob about 3/4 cup, no more. Flatten gently, but not so much that the patty disintegrates. It should be about a half inch thick. Fry until lovely and golden, then turn and fry the other side. This takes at least 5 minutes, so you really have to watch that nothing scorches. Don't put more than 4 pancakes in, if they are crowded they won't brown properly, they'll just get soggy.
I like them with a bit of sour cream, some like them with apple sauce. They are marvellous with ham or smokies, or corned beef.
My German neighbour used to make them with potatoes that were pureed, not grated, but I didn't like hers at all.
) - sunflower oil, like Frelga said! 
I think oil is more appropriate for frying Hanukah latkes, just because of the "miracle of oil part". I don't think butter is a concern, though, especially if the latkes are served with ham. 
This is about the dumbest thing I've ever heard. Pretty much.)
)