Boil potatoes for about 10 - 15 minutes. Use a small to medium sized potato (larger potatoes will take longer to boil). You can leave the skins on while boiling the potatoes. When the potatoes are fork tender let the potatoes cool until they can be handled comfortably.
Peel potatoes and place into a medium-sized bowl. Use a potato masher to mash the potatoes until they are of a smooth consistency. Turn mashed potatoes onto a large board. Make sure that you have let the potatoes cool enough so when you add the egg it won't immediately cook.
The potatoes are cool enough when you can handle them easily with your hands. Add 1 to 1 1/2 cups of flour to the potatoes, make a well on the center of the flour, and add 1 to 1 1/2 teaspoons salt. Add 1 egg to the flour, and mix the egg into the potato and flour mixture. When all of the flour has been fully incorporated into the potato mixture add remaining flour.
Mix until all of the flour is absorbed, this should have the texture of bread dough. Take a small portion of the potato gnocchi dough and roll into a long tube. Using a knife cut the tube into 1/2 inch pieces. To make the classic gnocchi shape take a piece of gnocchi and roll it across a fork to leave the impression of the fork tines into the dough.
Cook gnocchi by boiling in a large pot of salted water for about 2 to 3 minutes, or until the gnocchi floats. You can finish your gnocchi with a simple butter and Parmesan cheese topping if you like. For this take about 2 cups of cooked gnocchi, and place in a bowl, and add 1 1/2 tablespoons of butter, 2 teaspoons of Parmesan cheese, and mix together well.
This recipe makes quite a bit of gnocchi, you can leave the gnocchi until and in air tight container for up to 48 hours so you can cook it during the next day or two. You can also cook the gnocchi and re-heat it later. I think it is best to cook the gnocchi just before serving.