Boil potatoes, unpeeled, in plenty of water. Do not test them too often while cooking, as punctured potatoes can become waterlogged.
When thoroughly cooked, drain. Peel as soon as you can.
While potatoes still are hot, puree them through a food mill or potato ricer. You can mash the potatoes by hand, but then the gnocchi likely will be denser.
Add most of the flour to the potatoes. Knead into a smooth mixture. Add flour as necessary. Stop adding flour when the mixture is soft, smooth, and still slightly sticky.
Cut dough into four pieces. Shape each piece into a log roll about as thick as your thumb.
Shape the gnocchi. First, cut off a ¾-inch thick length. With lightly floured fingers and a floured fork, roll the cut-off piece across the tines of the fork.
Cook gnocchi
Bring 5 quarts of salted water to boil in a large pot.
Drop gnocchi into boiling water, in batches of about two dozen.
Gnocchi should rise to the top in a short time. Cook them about 10 seconds more, then remove with a slotted spoon.
Notes
Adapted from The Classic Italian Cook Book, Marcella Hazan.