In a medium size bowl, add the flour, salt, eggs, and water. Stir until a dough ball forms.
On a floured surface, place the dough and knead for 6-8 minutes. Add flour if the dough sticks to your hands, but try not to add an excessive amount (it won't need it). The dough should begin to feel more elastic in your hands as you knead.
Roll the dough out, it can be fairly thick (see photos). Cut the dough into thick strips, a pizza cutter works well here.
Bring a large pot of salted water to a boil. Add the noodles and cook for 4-6 minutes. The noddles will begin to dimple/prune when they are done (similar to your hands when you've been swimming a while). The best way to check is to remove a noodle from the pot and taste it. It should taste cooked, not gummy.
Once cooked, drain the noodles and add to a finished soup or toss in butter or sauce to enjoy.
If you wish to save your cut noodles until the next day (or up to at least 3 days later—I've never saved them beyond this, but you probably could), allow them to dry out for 10-20 minutes. Then cover well, or place in a container with a lid, and refrigerate until you're ready to cook them.