One afternoon I noticed a pool of coolant under my 300D. Further inspection revealed it was coming from the water pump. This car had all of the service records since new (it was a 1979 with 195,000 miles) and the words "water pump" didn't appear once so I believe it was original to the car.
The process is pretty straightforward, you don't even have to mess with the timing like you do in other cars (I'm looking at V6 Alfas here.)
1) Drain the coolant and remove the upper radiator hose.
2) Remove the bolts that hold the fan to the fan clutch. Use a box-end wrench but make sure it's a six point, NOT a twelve point. A twelve point sometimes won't get them off, I know-- I tried. Remove the fan, the fan clutch and the alternator belt. Removing the fan shroud isn't necessary the it gives you more access, I recommend it.
3) Remove the water pump bolts. Coolant will undoubtedly spew out so have something under the car ready to catch it unless you fancy having green snow on your driveway. Once the bolts are off, use a mallet to pound the water pump out of its housing.
4) Scrape off the old gasket material with a razor and dry it off. Spread gasket maker material around the pump and make sure not to go around the bolt holes. Put the new pump in its housing and tighten the bolts. Put the fan and its clutch back on (with a new alternator belt) and tighten those bolts. Put the radiator hose back on and fill the coolant. Check for leaks when it's all together.
While you're doing the water pump, change the thermostat as well. It's cheap, easy and a good precaution.