So, with that out of the way... Let's get this thing open!

There are seven screws on the back that you need to remove in order to separate the two halves. Six of them are standard philips head screws, and one is a strange little one called a "Gamebit." You can source a bit for it, if you want, but I find that you can turn it slowly with a pair of needlenose pliers!

 The red circles below indicate where the exposed Philips head screws are, and the blue circle is the Gamebit screw. There is also a screw underneath each battery cover, in the corner.

 There are three cables that go from the front half of the unit to the rear. On the rear case there are two small PCBs and a metal shield. Remove the screws from these (there are two screws in each PCB, and four in the metal shield), and remove them from the case.

Now, remove all of the Philips head screws holding the motherboard down, there are twelve (the two near for the cartridge connector are larger than the others).

At this point, you should have all the components removed! Hurray! You should save all of the bits and pieces for now, we'll be using them as the project progresses! Also, you can now remove the buttons from the front panel. Put those, their elastomer pads and all of the screws somewhere safe!