In the Italian tradition gnocchi are always meant to be dumplings. They are generally made with a potato - base with the addition of flour. The proportions of potatoes and flour may vary from one region to another, according to local customs and traditions, as well as to the type of potatoes used. In addition to potato based gnocchi, there are also other types of gnocchi made with flour, semolina ricotta cheese, spinach, or bread crumbs.
Gnocchetti are usually smaller than gnocchi.
NOTE: Idaho potatoes are the best to use. Do not choose early potatoes, as they are too watery.

GNOCCHI DI PATATE Potato Gnocchi
Basic Recipe:
Wash about 1 lb. baking potatoes and cook in lightly salted water (without peeling). It is best to start with cold water. The potatoes should all be about the same size. The cooking time will depend on the type and size of the potatoes. A rule of thumb to check when they are ready is to stick a fork into one or two potatoes and if it enters easily the potatoes are ready. When the potatoes are cooked, drain, peel and mash them through a potato ricer, (do not use a food mill, it will make a sticky puree impossible to work with) and place on a pastry board or a marble surface. Should the resulting puree be too watery, put it back over the stove over moderate heat and let it dry well, stirring constantly.
It is important to have a dry puree, otherwise it will be necessary to add too much flour, which will result in heavy, doughy gnocchi. Add a small amount of salt and as much white flour as necessary to have a soft dough that does not stick to your fingers. It is not necessary to mix the dough for a long time; it is sufficient just to blend the ingredients. Cut a piece of the dough and, coating your hands with flour, roll the dough into a long cylinder about the thickness of your index finger. Then cut the cylinder in pieces about 1-inch long. By pressing with the tip of the finger against the board, sweep the dough lengthwise, toward you. This will cause each piece to curl up, taking the shape of a little shell. You may also use other utensils for this purpose such as the back of a cheese grater. In this case, the gnocchi will be ridged and curled. It is not absolutely necessary to give it one shape; they may be simply cut into nuggets of any desired size. Handling the gnocchi as little as possible, quickly ontinue this operation until all the dough is used. Place the finished gnocchi in a flat pan sprinkled with flour without putting one on top of the other. Cook as soon as possible. A variation to this basic method is to add one or two eggs to the potatoes and flour dough. The eggs will make the mix harder, more consistent. In some cases this is a desired result especially if large amounts have to be prepared or if they have to be made long before the final cooking. In this case the gnocchi will not be as soft, they will have more of a bite.

How to Cook Gnocchi
Gnocchi should not be prepared too far in advance before cooking. To cook gnocchi it is preferable to use a large pot with a wide bottom, so that the heat underneath can spread well, allowing the water to return quickly to the boiling point again after the gnocchi have been added. This is important because, if allowed to stay in the water for too long, the gnocchi can break up and absorb too much water. Add the gnocchi to the boiling water all at once and stir gently. Let cook until the gnocchi float to the top (a few minutes are enough), then lift them out of the water with a skimmer (do not use a colander). Place in a preheated bowl. Toss with the desired sauce, add parmigiano, if necessary, and serve immediately.

Sauces for Gnocchi
They are many sauces for gnocchi, and they vary from region to region. You may use melted butter flavored with sage, tomato sauce, mushroom sauce, bolognese ragù pesto, or one of a variety of meatbased sauces such as lamb, veal, beef or pork, as well as the juice resulting from roasting or braising beef or with Gorgonzola, Fontina, etc. Sprinkling the gnocchi with grated Parmigiano is a must, except for a preparation with cheese, regardless of the type of the sauce used.