We made this type of pasta in both the cooking classes I attended when I visited Italy. This simple recipe can be rolled out and cut into spaghetti, vermicelli, fettuccine, linguine...made into ravioli (pictured below), farfalle... Or other shapes if you're really creative and have a lot of time. In one of the classes, the chef scoffed at using a pasta rolling machine, preferring to do everything by hand (which really doesn't take long if you're only making a single recipe -- below, serves 1 or 2). In the other class...the chef used one! :)
2/3 C flour*
1 large egg
(Lots of pasta recipes include a little olive oil and/or a pinch of salt. Neither of the chefs in my two cooking classes in Italy did -- but I have experimented with it since then. I like a little olive oil.)
Mound the flour on a flat surface and make a well in the middle. Crack the egg into the middle of the flour well. With a fork, beat the egg and begin mixing in the flour. As a dough begins to form, use your hands to knead the dough until all the flour is incorporated and the dough is very smooth.
Roll the dough very thin; cut or shape into desired noodle size/shape. Place in boiling water for 2-4 minutes.
Cooking time may be slightly longer if you stuff the pasta (e.g. ravioli) or if it's folded or gathered like with a farfalle shaped noodle ('bow-tie' pasta); but with fresh pasta it's really quick.
*In Italy, the recipe was given in grams...so if you have a kitchen scale: 100 grams of flour. Generic, all purpose flour works well with this pasta. In one of the classes we made another pasta with semolina flour; I'll try that out and post it soon. :)