Eric's post is pretty comprehensive. You might want to consider this advice that was given on the alfadigest:
(Credit to Dean of Florida on the Alfa digest for this, I hope he doesn't mind me reposting it)
"The alternator (70 - 75 amp) from a '90 - '94 Spider will bolt on to your
'81. I've used that unit on both my '74 and '87 Spider's without
trouble. Of course the biggest improvement came on the '74, as it
originally had a 35 amp unit. Now I can use the H4 high beams, defroster fan, wipers, and the stereo all at once. I had one tiny problem on both cars, though, which was easy to remedy. The fan on the new alternator (at
least on both of mine) was ever-so-slightly larger than the original, so it rubbed (barely) on the washer under the head of the main mounting bolt, and also slightly on the bottom edge of the adjustment bracket. A little filing, of the washer and the bracket fixed things right up.
Besides the extra current output, the other difference is that the new alternator has its voltage regulator built-in. For the new alternator wiring, first remove the old regulator and the harness that connected it to the old alternator. Keep them or trash them, but they don't need to be on the car any longer. There will be one wire (green) left unattached in the car's harness, which is for the alternator light. Run a green 14 ga. jumper from it to terminal 'D+' on the new alternator. Finally, run a red
8ga. wire from the 'B+' on the alternator to the '+' side of the battery, using ring connectors on both ends. Since your battery is in the trunk, run the wire along the rear edge of the chassis crossmember to the big '+' terminal on the starter. My '87 has a junction on the left inner fender, where all the high-current 12V+ leads converge, but I don't think your '81 has that. If it does, use that as the termination point of your alternator's B+ wire. The reason for the new, larger wire is two-fold. First, you've got more current, so you need more wire. Second, the original wire always was too small, and by now, it's probably corroded.
Also, I should tell you that others have used GM/Delco, Ford, or Chrysler alternators of various current output, which are usually available for less than $50. Some minor machining is usually necessary, and I didn't know if that was an option for you. I prefer to stay with a Bosch, anyway, as it's 100% bolt-on, and it looks original.
Here's a source for the alternator:
$83, including core charge, and a 3-year warranty. Don't forget to
disconnect the ground wire from your battery before doing anything, and ask if you have any questions.