I replaced my alternator on Saturday. The bearing had seized and broke the belt. I got a rebuilt Bosch from Amazon for $222 and two gallons of 50/50 pre-mixed coolant for $28.

The instructions by the original poster are pretty straight forward. Remove the intake duct and the air tube from air cleaner to engine throttle body. Remove undertray.

What I ended up doing to make it easier/less messy was just drain the radiator. Do this by removing the drain plug on the driver's side bottom of the radiator. Mine was a little blue plug - BMW did something nice by putting a little retaining strap on the plug so you don't have to worry about dropping it into the bucket that the coolant is draining in.

After you drain the coolant remove the coolant hoses/fittings as shown in the original poster's pictures. Loosen the belt tensioner, take the wires off the alternator (after unhooking your battery +/- connections. Unbolt and remove old alternator.

Clean area where alternator goes, bolt new alternator in. Now is a good time to also replace your air conditioner compressor drive belt. Reinstall water pump/power steering/alternator belt and set tension (there's a DIY on how to do this elsewhere on xoutpost.).

Reattach coolant hoses and refill system with coolant (mine took about 2 gallons). Put the intake tube and duct back on. Test drive. Check coolant level again once the engine cools down - don't remove the top tank cap when the engine is hot or you might get sprayed with hot/boiling coolant.

Now you once again have a happy wife, happy life.