Freeze the Pasta
The best way to store fresh homemade pasta is to freeze the uncooked cut pasta shapes. You can store them in the freezer for about 2-3 months and just toss them frozen in boiling water to cook. Do not thaw frozen pasta as it would become sticky. For this very same reason, do not freeze an entire pasta dough as it would be sticky and difficult to handle once thawed. Just freeze the cut pasta shapes.
How To Freeze Pasta
Cover a tray with parchment paper (the tray needs to fit in your freezer) and individually place the cut or stuffed pasta shapes on the tray without stacking them on each other. If you made long pasta, swirl it into nests. Dust the pasta with flour (coarse or fine), cover the tray with plastic wrap, and place it in the freezer for a few hours.
Once the pasta has completely frozen, remove it from the tray and store in freezer bags (since the pasta has hardened, it will no longer stick to each other). Remember to write the date on the bag.