Hi Nick, I regularly make fresh pasta by hands without pasta making machine. Though I am sure there are much improved versions around these days, once I tried it many years ago, and found that cleaning and washing each and every bits with particles of dough stubbornly stuck in every little corner was more of a hassle than a little elbow grease I put into for kneading.
And every Italian mammas have done this for ages without any machine, so if you don't have the appliance don't worry too much...
Here is what I do...
the main ingredients are flour, eggs and water.
Use one medium egg to every 100g of flour (about 3,5oz).
Keep a small jug of water and additional flour nearby and handy.
Wash your hands well.
Pile the flour on a flat board, making a well in the middle.
Crack the eggs into the well, then carefully mix in the flour from the top edge into the egg mixture, gradually blending everything together. (At this point some people stir the eggs with folk before starting to blend in the flour, but I usually don't bother with that) Don't worry if egg escapes and oozes outside, just push it back up with the outside edge of your hand and keep blending it with the flour.
Once the eggs and flour are blended, start kneading vigorously and evenly, for at least 15 minutes until the dough is completely smooth and elastic.
You have to feel the dough while you are kneading. If the dough is too sticky and gooey, add a little flour. If the dough is too dry and hard, add some water. At the beginning of the kneading the dough may feel quite unmanageable, but that is also normal, keep on working it and adjusting the texture with water or flour, sooner or later it will become much "tamer"!!
Form a ball and cover it with a wet cloth, let it rest for about 30 minutes.
Dust well the board with flour.
Then flatten the dough with a rolling pin evenly, dividing the dough in a few pieces as needed, to about 1-1,5mm thickness.
At this point, you can also make it into lasagna/cannelloni sheets, or cut into thin strips to make tagliatelle. It is (at least for me) almost impossible to stretch the dough into a regular shape (rectangle or circle), if the odd pieces are left at the edges, that is quite normal and you can also use that, cut them up in anyway possible and cook it and enjoy that with your choice of sugo. (they also have an official name in Italian "maltagliate", or badly cut, but widely used anyway, after all, they taste good just as well!)
For making ravioli, there are two options. If you have a proper ravioli cutter, you can arrange the filling on a stretched sheet, small pile at a time, then wet where that is going to be the borders of the raviolis with a brush, then cover with another sheet, then press where that is going to be cut rightly with finger. then make the cut.
Alternatively you can use a glass or biscuit cutter or something round to cut out the dough, and fill each round piece of the sheet with the filling, again wet the border and press together the border evenly. (you can either fold over the round sheet and make a half moon shape, or use 2 sheets over each other and make a round one.)
The important thing is not to get too overzealous with the amount of filling as they could easily explode while being cooked in water.
When you cook it make sure to use plenty of water and make it come to a full boil, also cook one portion at a time at most (not to cook too many at a time as the water temperature will go down too low). when they rise to surface, they are ready.
For fillings, you can use your imagination and experiment with different things, I personally like ricotta with either different kind of mushrooms or spinach and some additional cheeses, or chopped prosciuto or speck.
If you are not going to cook them immediately, dust them with flour and store them in a fridge.
Yes, it is a bit of work but also enjoyable and freshly made pasta is definetely worth all the effort. Give it a try, and buon appetito!!