So everything should come off of the fan housing. The coil, for instance, comes off. Now pull the fiberglass fan shrouding up enough so you can start removing the fan housing. The bottom of the fan housing rests on a short peg, which centers it and locates it, so it has to come out over this. Looking in you will see that to get the assembly all the way out you will have to disconnect some wires.
Most alternators have a ground strap which is attached to one of the engine case peripheral studs.
Reaching in, remove the nut on that stud bolt to free the connector. Also, there are some wires coming out of the back of the alternator. If you don't have a simple connector, make a diagram so you will know which wire goes where. Take the whole assembly out. My recollection is that the same nuts which hold the plastic cover on serve as most of the nuts which hold the alternator onto the fan housing.