Ingredients: 1 egg per 1 cup of all-pupose flour.
Two eggs and two cups flour makes enough pasta for four people if you have a salad or something on the side, or two people (maybe with leftovers) if dressed pasta is the main event, and that is the amount of past I'm making in the tutorial below.
First, pour most of your flour out onto your work surface in a mound. Reserve some of the flour -- you can always add more later. Use a fork or your hands to make a little or "well" the middle of the mound -- this is where your eggs will go.
Using your fork, whisk the eggs to break them down, then begin gradually stirring in the flour from the sides of the "well," incorporating it into the egg. Feel free to use your (clean!) hands to do this. Eventually it will be easier just to use your hands to knead all the ingredients together.
When you have brought all the egg and flour together, the dough may look a little dry, but you are going to let it rest, which gives it a chance to absorb a little more moisture from the egg, and also lets the gluten in the flour relax. Shape it into a ball and wrap it tightly in plastic wrap so that moisture will not escape. Place it in the fridge and let it relax for about 40 minutes.
When the dough has rested, take it out and divide it into fourths (I use my bench scraper). Work with the dough one quarter at a time, keeping the rest tightly wrapped. I don't know if I can emphasize that enough -- if your dough isn't well-wrapped, it will dry out and become unworkable. Take your first chunk of dough and flatten it out into a rough rectangle.
Begin rolling your dough at the widest setting (on my machine,this is the lowest number on the dial -- look to see that the rollers are as far apart as they can go.) If my dough seems a little dry, I fold and re-roll the dough on the first setting a couple times to get the pasta to smooth out. Then, all you have to do is gradually roll the pasta thinner and thinner, until it is your desired thinness. I always roll mine as thin as possible, but that's just my preference. For noodles, you can use the cutters on the machine, but I like the rustic look of handcut noodles -- you can also buy things like ravioli attatchments, but again, I think doing it by hand is probably just as easy, and I think the handcrafted look is charming.