Add whole eggs, matzoh meal, onions, and salt and pepper to taste. Mix together thoroughly. It'll probably require using your hands.
Heat 1/2" of oil as hot as it will get in skillet.
Form four large balls of potato mixture. Squeeze out most of the water. Pack them as you would pack hamburger. Gently flatten them into 1"-2" thick patties. Slide patties into hot oil. Four should approximately fill a large skillet. Once bottom is browned, flatten patties further (to about 1"-1.5"). When the bottoms are golden brown, about five minutes, flip patties and fry other side until golden brown, somewhat less than five minutes. Cooking times vary greatly by water content of patties, temperature of the oil, and factors I don't know. Be alert after the flip or they may burn.
Remove from oil and drain on paper towels. Serve with apple sauce. Other good toppings are sour cream, apple butter, jam, or corned beef.
If there is left over potato mixture, make more patties and repeat. Add more oil before cooking each successive batch.
These freeze adequately and can be microwaved (but are a little soggy) or thawed and baked in a toaster oven.
Unfortunately, the exact measure of ingredients is really not accurate. The amount of matzoh meal and eggs will vary by the water content of the potatos. More will make the patties bind better, although they often should be on the verge of breaking apart anyway. Once they are cooked, they'll hold together much better. Onion amount is to taste. Doubling the amount of onion, or leaving it out entirely works fine, just gives a different flavor. I typically make huge batches, ten pounds or so, at a time. It's important to add more oil after each batch of four or the latkes may burn.
Many prefer different styles of latkes; perhaps with no other recipe have I seen so many dogmatic claims that "my recipe is the only real one." I think this is a result of different families' having different traditions making them. I particularly like big thick latkes with very coursely grated potatos. Others think that the potatos must be ground very finely so as to make thin pancakes. To each his own.