In a large bowl, combine the flour, salt, water and olive oil. Using a clean hand, mix well to form a dough. On a lightly floured surface, knead the dough for 5 minutes. Wrap the dough in cling film, and leave it to rest in the fridge for at least an hour.
When the dough has rested, unwrap it and cut it into 4 pieces. On a lightly floured surface, roll out the dough with a rolling pin. After every few rolls, turn the sheet of dough over, and rotate it through 90 degrees, then continue rolling. You want to end up with a very thin sheet, in a roughly rectangular shape.
Lightly dust the sheet of pasta dough with flour, then loosely roll it up. Cut the roll into strips (wider strips will give a wider tagliatelle). Unravel each piece, and set aside onto a floured board.
Repeat with the remaining three balls of dough.
When you're ready to cook the pasta, bring a large pan of water up to the boil, flavoured with a generous pinch of salt. Add the pasta, and cook just until it starts to float - anything from 20 seconds to a couple of minutes. Don't overcook.
As soon as the pasta is cooked, drain it and serve with your favourite vegan pasta sauce.