How to Make Fresh Egg Pasta

Pour the flour into the mixing bowl with a pinch of salt and the egg(s) and oil if using. 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.
Switch to the dough hook and continue to mix. At first continue at a slow speed, then turn it up a notch to a moderate speed (setting 3 or 4) until the dough sticks to the hook and forms a smooth surfaced, uniform ball.
Ideally, the dough should be pliable but not at all tacky. If you find the ball is very sticky and wet, add a bit more flour until the dough becomes firmer. If on the other hand dough is too dry to form a ball, add a bit of water.

Add you ingredients to the processor bowl and pulse until they form a ball, making adjustments if need be as described above.

Pour the flour in a mound on a spianatoia or other dry surface. Make a well in the middle of the flour. Add your eggs, salt and oil into this well.
With a fork, begin to whisk the ingredients in the well, incorporating the flour at the sides of the well little by little.
When the mixture get too dense to mix with your fork, begin to use your hands. Incorporate more and more of the flour until you have a pliable ball of dough.
Place the dough on a pasta board (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.)

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.
(If you short on time, it is not an absolutely necessary step.)

You can roll out the dough using the pasta roller attachment of your standing mixer, or a hand cranked pasta machine. Begin with the roller set at the widest setting.
Divide the dough into as many pieces as the number of eggs you used. Take one piece and flatten it out with your hand or a rolling pin. Then pass it through the roller, which will turn the dough ball into a rather thick sheet.
Fold this sheet in two and let it go through the roller yet again. If need be, lightly flour it so it doesn't stick to the roller. Repeat as needed until the pasta has reached a smooth consistency.
When the pasta is smooth, turn the roller to the next, slightly narrower setting. Keep passing the pasta sheet through successively narrower settings, one by one, until you reach the thickness you need for the type of pasta you're making. Flour as needed to prevent sticking.
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, lay out the pasta sheet to dry on a towel or (my preferred method) on a drying rack. The rack will allow air to flow on both sides of the pasta, so it will dry more quickly and evenly.
If using a towel, it's a good idea to turn the sheets over every once and while so they dry evenly.
The pasta is dry enough when it feels 'leathery' to the touch but not brittle.
NB: For stuffed pastas like ravioli, you do not want to allow the pasta to dry. Rather you need to work as quickly as possible once the pasta is rolled out into sheets. The pasta should remain moist, so that the top and bottom of each pasta 'pillow' sticks together.

Once dried to the right point, pass the pasta sheets through the cutting attachment of your mixer or pasta 'machine'.
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 the strands out on a floured surface (or back on the rack).
Depending how thick or wet 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.