Place the flour on a clean work surface and shape it into a mound. Make a well in the center and crack the eggs into it. Add the salt and olive oil. Use a fork to slowly blend the eggs with the surrounding flour.
Once the mixture starts to come together, use your hands to knead it for about 8 to 10 minutes until the dough becomes smooth and elastic. If the dough feels too dry, wet your hands with a few drops of water. If it sticks, sprinkle a little flour.
Shape the dough into a ball, wrap it tightly in plastic wrap, and let it rest at room temperature for 30 minutes.
After resting, divide it into 4 pieces and roll each out on a lightly floured surface using a rolling pin until very thin (between 1/8- to 1/16-inch thick). Alternatively, use a pasta roller to make the sheets.
Cut the rolls of pasta into strips roughly 1/4-inch thick, depending on what pasta you are making.
Bring a large pot of salted water to a boil. Place your freshly cut pasta into the boiling water and cook for about 1 to 3 minutes until tender. Drain the pasta and serve with your favorite sauce.