True, there are lots of places now that you can get fresh pasta-- but there's just something so satisfying about making your own. It's not hard, and you feel like an Italian grandmother (without the mustache!). You can go even more Old World by piling the flour on your counter, making a well for the eggs and mixing it all with a fork or your hands. I don't need to go quite that "artisan"-- I always end up getting egg everywhere that way. A stand-up mixer works great.
I have a crazy electric pasta machine that I got for free-- but worth the investment if you plan on making pasta on a regular basis... I'm sure you can find one on ebay if you keep an eye out. Or, you can buy a hand-crank machine, which also works perfectly fine-- or simply roll it out by hand (if you roll by hand, make sure you let it rest for a couple of hours to make it easier).
A couple tablespoons butter, for serving (optional)
Fit the paddle into your mixer. Put the flour and salt into the bowl, and turn it on briefly to mix. On the lowest speed, add your eggs, one at a time, followed by the oil. Crank up the mixer to medium, let it go until you have coarse grains of dough in the bowl—kind of like a pie crust before it’s gathered into a ball (it should take between 30 seconds and a minute).
Replace the paddle with the dough hook and knead in the bowl for about five minutes. It should look relatively smooth—not sticky, not crumbly. If it does look sticky, add some flour, a teaspoon at a time until it looks smooth. If it looks crumbly and ragged-looking, add cold water a teaspoon at a time.
Then take it out of the mixing bowl, and knead it by hand on the counter for a few more minutes. You should have a firm, smooth, pale yellow ball of dough. Wrap it tightly in plastic wrap, and let rest at least 30 minutes, preferably 1-2 hours (Resting the dough allows the gluten in the flour to relax, and the dough becomes much easier to work. If you are having trouble rolling out your dough, simply let it rest a little longer).
After the dough has rested, cut it into 4 pieces. Put three of them back in plastic wrap (to avoid drying out), and flatten the 4th into a disk with your palm or rolling pin. If you have a pasta machine, set it so that the rollers are at the widest setting (or you can just roll out with a rolling pin).
Feed the disk through the rollers a few times on this setting, folding it in half each time before it goes through the rollers. It may come out with ragged edges or with holes in it. That means the dough hasn’t been kneaded enough. Don’t worry. Patch the holes with bits torn from the end, and feed the dough back through the rollers. If the edges are ragged, fold the ribbon in half lengthwise. If it is sticky, sprinkle some flour over the pasta sheet before putting it through the rollers. If the dough comes out in a weird shape, just fold it into a flat square before rolling it through again. You’ll know when it’s rolled enough, because the dough will be smooth and satiny. The nice thing about pasta dough is that it isn’t delicate, like pie crust—if it’s not right, keep working with it.
After you have a smooth, satiny stretch of dough, narrow the opening by one notch. For the next couple of “notches”, run it through twice: once, fold in half, then again. For the final couple settings, just once through is fine. (I go all the way to 2nd to- last-thinnest, because I like a bit of “bite” to the noodle, but if are looking for a thinner, more delicate noodle, go ahead to the end).
Now that you have a nice sheet of dough, it’s time to make noodles!* Either run the sheet through the noodle-cutter attachment, or cut them yourself. Either way, cut the sheet into “noodle-lengths”—about the 8-10 inches each, before you cut into “noodle-widths”. If you hand cut the noodles, sprinkle some semolina flour over the whole sheet (it acts as “ball bearings” and keeps your pasta from sticking to itself), then fold it into fourths. For pappardelle, cut the pasta into 1 inch wide ribbons (a pizza cutter works great), then unfold the noodles.
Once you have noodles (either hand or machine-cut), let dry about 5 minutes, then sprinkle copiously with more semolina and make little “nests” on a baking sheet. Don’t worry about using too much semolina—the more the better. It just washes off the instant you plunge the noodles into the water, and it definitely keeps your noodles separated.
Now go back and roll out the other sections of dough. When you have finished all 4 sections of dough, wrap your noodles tightly in plastic and refrigerate if you aren’t using right away. Pasta is always best the day of—or the next day. If you aren’t going to eat it right away, you can always freeze it. Keep it wrapped tightly in plastic or Tupperware no matter what. Use refrigerated noodles within a day or two.
When cooking the noodles, make sure you use a big pot with plenty of salted water. Bring the water to a vigorous boil, and add your pasta. Once the water has started boiling again, start checking your pasta. It should be beautifully pliable, with no hard core to it (look for the “white line” of flour in the very middle). Pour the pasta into a colander (but save a bit of the pasta water, in case you need to adjust the consistency of your sauce). Add a couple pats of butter (if using), and toss the pasta to coat, then add your sauce.