If you are preparing the pasta dough by hand, meaning you don't have a stand mixer, then skip below to the "notes" section for instructions.
To the bowl of your stand mixer, with paddle attachment fixed, add the eggs, flour, olive oil, salt and water. Mix on low speed for 2-3 minutes, or until the dough starts to come together. Switch to the dough hook attachment, and knead the dough for 4-5 minutes or until soft to the touch and pliable. If the dough is too sticky, add flour in small increments. If the dough cracks or seems too dry, add water in small increments until you reach the right consistency. Once your dough reaches the right consistency, form it into a disk and wrap it tightly in a piece of plastic wrap. Set aside for at least 30 minutes or up to 2 hours.
Unwrap your dough and place it on a generously floured surface. Cut it into 4 equal size pieces. Flatten them out with your finger tips (image above).
With the roller attachment fixed to your stand mixer and set to the lowest setting (1 for KitchenAid), insert the dough through the top. Once it goes through, fold the dough in half. Flour your dough and run it through a second time. Repeat this step, if necessary, flouring when needed, until the sheet is smooth and elastic. Increasing the setting by one step (2 for KitchenAid), insert the sheet again, but don't fold it over this time. Increasing the setting by another step (3 for KitchenAid), insert the sheet once again. Repeat these steps up to your desired thickness. For example, if preparing spaghetti, you will want to go to the 6th setting. (See steps above in the post for instructions on rolling dough out by hand).
Change the attachment to the appropriate cutter. Generously flour the dough, and insert the dough carefully through the top of the attachment. Once you have the pasta cut, toss with a little bit of flour to prevent it from sticking. Set aside, covered with a damp paper towel until ready to cook.