When making fresh home-made egg pasta, variously known in Italian as pasta fresca or pasta fatta in casa or pasta all'uovo, I usually make life easy for myself by using my trusty KitchenAid mixer to form and knead the pasta dough and then the pasta attachments to roll out and cut the dough into various pasta shapes.
An easy to remember rule of thumb is to use 1 egg per 100g of flour for each person. If you are using imperial measurements, the rule is 1 egg per cup of flour per person. These rules of thumb, however, are not at all exact, as the results will depend on the exact size of the egg, the quality of the flour, even the humidity in the air, so be prepared to adjust as you go along.
Pour the flour into the mixing bowl with a pinch of salt and the egg(s). To make the rolling and cutting easier later on, you can add a drop of oil, before adding the eggs although purists frown on this. Attach the dough paddle.
Turn on the mixer mix at slow speed (setting 1 or 2) until the the eggs are well incorporated. The dough may look rather crumbly at this point, but not to worry.
Switch to the dough hook and continue to mix, first continuing at a slow speed, then turning it up a notch to a moderate speed (setting 3 or 4) until the dough sticks to the hook and—hopefully—forms a smooth surfaced, uniform ball. But depending on various factors, including the exact size of the eggs and the ambient humidity in your kitchen, one of two things may happen: either the ball will be very sticky and wet, in which case you can add a bit more flour until the dough becomes firmer, or the dough will remain too dry to form a ball, in which case you can add a bit of water.
You can use more or less the same method for making pasta dough in a normal food processor: Add you ingredients to the processor bowl and pulse until they form a ball, making adjustments if need be as described above.
You can also form the dough the old-fashioned way, entirely by hand: pour the flour in a mound on a spianatoia or other dry surface, then make a well in the middle of the flour (this is called a fontana, or fountain, in Italian). Add your eggs, salt and oil into this fountain. With a fork, begin to whisk the ingredients in the well, incorporating the flour at the sides of the well little by little. As the mixture becomes too dense to mix with your fork, begin to use your hands to incorporate more and more of the flour until you have a ball of dough.
Whichever method you use, once you have your ball of dough, place it on a lightly floured spianatoia or other dry surface and knead it by hand for a few minutes until the dough has reached the right consistency, smooth and pliable and yet still firm. (If you find that the dough is too wet, sprinkle it with flour and knead the additional flour into the dough.
Then allow the dough to rest for 30 minutes wrapped in plastic wrap or a plastic bag. This rest will 'relax' the dough and make it much easier to work with, but if you lack time, it is not an absolutely necessary step.
Then put the pasta roller attachment on the mixer (or a pasta 'machine'), set at the widest setting and, taking a piece of dough corresponding to one of the eggs used to make the dough (in other words, if you used 3 eggs, cut the dough into three pieces), flatten it out with your hand or a rolling pin and then pass it through the roller, which will turn the dough ball into a rather thick sheet.
If the pasta has a smooth consistency (which is should if it has been properly kneaded and rested) then lightly flour the pasta sheet, turn the roller to the next, slightly narrower setting. (If not, fold the pasta sheet and pass it through the widest setting once again, and repeat as needed.) Keep passing the pasta sheet through successively narrower settings, one by one, until you reach the thickness you want, which will depend on the kind of pasta you are making. Repeat the process with the other pieces of dough, which you will have kept wrapped in plastic so they don't dry out.
For most kinds of pasta, such as tagliatelle, taglierini or fresh spaghetti, lay out the pasta sheet to dry on a towel or (my preferred method) on a baking rack. The rack will allow air to flow on both sides of the pasta, so it will dry more quickly and evenly. In either case, however, it is a good idea to turn the sheets over every once and while so they dry evenly; the top will always dry more quickly than the bottom, even when using the rack. The pasta is dry enough when it feels 'leathery' to the touch but not brittle. If it is not dry enough, the pasta stands will tend to stick together when you cut the sheet, while the dough will become unworkable if dries out. (If you notice that splits are beginning to open on the sides of the pasta sheets, then it is getting too dry, but if you act quickly enough, the dough can still be used.) With some practice (and a few inevitable misfires) recognizing the right degree of dryness will become second-nature.
Once dried to the right point, pass the pasta sheets through the cutting attachment of your mixer or pasta 'machine'. The KitchenAid mixer pasta set, as well as most pasta 'machines', come with two cutting attachments, one for thin pasta like spaghetti or taglierini and one for ribbon pasta like tagliatelle or fettuccine. (The one for thin pasta will be the roller with cutting blades at narrow intervals looking something like a comb.) Other pasta shapes need to be cut by hand.
As the pasta sheet passes through the roller, catch the strands of pasta with your open hand and gently hold them up so they do not fold onto each other. Lay them out on a floured surface (or back on the rack). Depending how thick the pasta sheets are, it is possible that some of the strands will stick together. If this happens, then you can just gently pull the strands apart. It's a bit tedious but not too difficult.
For stuffed pastas like ravioli, however, you do not want to allow the pasta to dry, but rather you need to work as quickly as possible. The pasta should remain moist, so that the top and bottom of each pasta 'pillow' sticks together.
See the recipes on this blog for specific instructions on rolling out and cutting particular types of fresh pasta.
NOTES: The best kind of flour for making most kinds of fresh pasta is called farina "OO". It is made with a soft wheat (farina di grano tenero) that has been very finely ground and all impurities removed. (In Italy, flours are categorized from "OO" to "O" to 1 and 2, going from the finest to the coarsest If you read Italian, this Wikipedia article explains the system.) Farina OO gives the pasta a lovely texture, somewhat firm but not nearly as firm as store-bought pasta. The problem with much so-called 'fresh pasta' that you may buy in stores outside Italy is that they are almost always made with semolina flour, which is the kind of flour used to make 'industrial' pasta like spaghetti, penne and the like. It gives the fresh pasta a hardness that is not characteristic of fresh pasta.
Farina "OO" is available in many Italian specialty stores, as well as (in the US) online. If you can't find this kind of flour, regular 'all purpose' flour will do. And some cooks like to use a blend of all purpose and cake or pastry flour to try to approximate the texture of farina 00. Some cooks use pure pastry flour, which I have never tried but suspect would be too soft. I have not experimented with these blends, so I would not want to comment.
There are other sorts of fresh pasta that require other sorts of flour: orecchiette, for example, are made with a blend of semolina and all purpose flour. One of my favorite winter pastas, pizzoccheri, are made with a mixture of buckwheat and white flours. Individual recipes will specify the kinds of flour to use but, unless specified otherwise, you can assume that farina 00 is the flour you should prefer.
