The first task required for disassembling your new (and probably filthy) alternator is to remove the drive pulley. The nut holding this on will probably be too tight to allow you to simply hold the pulley and break it loose, so the tool of choice for this seemingly simple task is an impact driver, probably air driven. If you don't have this tool, save yourself some grief and go to your usual mechanic and offer a couple of bucks for him to break it free. It will only take him the time he needs to pick up his air tool and a proper socket plus 10 seconds to use them, so he shouldn't charge much. You may want that pulley to attach some blades to later, and if you put it in a vice and try to remove it yourself without an impact tool you will probably ruin it.
Now put a few drops of penetrating oil on the drive shaft so that it runs down to the bearing inside the aluminum case. You will be removing this bearing later, and it will probably be stuck. If you are incredibly lucky (more than me, anyway) the bearing will come off the shaft and stay in the case when you remove it. In real life this will only happen if you already own a good bearing puller, however.
Next, take the thin cover off the other end of the alternator and disassemble and remove all the parts you see within. Be careful to not destroy anything, you will be using the diode assembly later and perhaps a few other things, so save everything. Don't worry too much about how you will put things back together, we'll get to that part later. The diode assembly is the largest part in there, and is made mostly of copper. The large output terminal is attached to it, and it is held to the alternator proper with three big bolts, four terminals around the edge, and possibly some miscellaneous things like the voltage regulator and brush assembly. Strip it all out.
Things will now get interesting, because you need to take the case apart, and it doesn't want you to. Begin by removing the nuts from the bolts holding the case together (four, around the edge). Don't worry about the three bolts protruding from the case end that were holding the diode assembly in place. At this point the only things holding the case together are the bearings at either end of the rotor shaft, so we need to apply an even force separating the case halves without canting it enough to damage the bearings. I use several old kitchen knives for this, as shown below. (But I just discovered that there is a better way shown in this video: https://www.youtube.com/watch?feature=player_embedded&v=qlccLGgvIW0)
It would be nice if you can get this case to separate without damaging the surfaces where they join too much, but my experience has been that this is very difficult to actually do. The alternator will tolerate a small amount of damage to these edges, however, as long as this damage doesn't prevent the case-halves from closing completely back up later. GENTLY tap the knives into the split to force the case-halves apart. If you can get enough clearance to get a bearing puller in there and finish the job, lucky you! Eventually, after much sweat and foul language, you will be able to separate the case halves. The rotor will remain in one of the bearings, but at this point a bearing puller should suffice to finish removing it.
If the bearings remained in the case halves you are one lucky guy and can leave them there. If not you will need a bearing puller of an appropriate size to remove them. DO NOT pry at them with a screwdriver or any such instrument, they need to be pulled straight off the shaft or they run a strong risk of damage. They are fairly easy to find replacements for, however, and if you do damage one you might as well replace them both. If they seem rough you should also replace them. I've taken several of these alternators apart, though, and so far I have not found a single bad bearing.
You should now have a nice stack of utterly filthy parts, so your next job is to clean them all up. I use cheapo "engine degreaser" which I spray on, let it soak for a while and then rinse off. A little work with a brush is a good thing as well. After you are done, blow everything dry with an air hose if you have one. Otherwise you could try a hair dryer on low heat.