Lightly beat eggs with water, oil and salt. Put the flour in the bowl of a food processor. With processor running, slowly pour the egg mixture into the flour mixture and process until the dough forms a ball. If the mixture does not form a ball, add more water, a little at a time, until it does.
Remove dough from the processor and knead for two minutes. Allow the dough to rest at room temperature, covered with plastic wrap, for 30 minutes.
Roll the dough into a 3" thick log and cut it into six equal disks. Feed the dough through a pasta maker, starting at the widest setting and working it through to the thinnest. Cut the dough by hand for a rustic look, or process through the fettuccine cutter on the pasta machine. Dry pasta on a rack or in nests on a sheet pan sprinkled lightly with flour.
Hand method for smaller quantities:
½ T olive oil
Lightly beat egg with water oil and salt. Place flour on work surface and make a well in the center. Add the egg to the well using a fork or your fingers slowly stir the egg in the well gently pulling in flour as you go. When the mixture becomes too much for the fork you will need to switch to your hands. Continue working in the flour until a soft dough ball can be formed. Clean your work area making sure that any hard flour bits are removed keep the clean flour to the side. Pat the dough ball in the flour and knead until completely incorporated, continue this process until the dough no longer feels sticky. Allow the dough to rest at room temperature covered with plastic for 30 minutes. Follow the directions above to finish.
Fresh pasta cooks very quickly! It will take about 1 minute at sea level, 2-3 minutes at 5,000 feet.
Never rinse pasta unless it is to go into a salad, in which case it should be dressed and served as soon as possible.