Dismantling the Gamecube (Taking apart the Gamecube)
First thing you'll need is the screwdriver. I got mine from ebay. Two types are available, the screwdriver and the bit. I think the bit is probably more useful, you can put it on a powered screwdriver that way.
There are 4 screws holding the base to the top, after removing those screws the top just slides off.
Next you remove all the screws holding the cd player to the motherboard. It's worth noting that the nintendo design is very technician friendly. All the major components use sockets and are easily removed.
With the CD removed you can unclip the front and back panels. The front panel holds the controller ports and memory slots. Once those are removed, you remove the 6 screws holding the motherboard to the bottom board. There is some circuitry below the motherboard that I didn't bother dismantling.
Once you have removed the motherboard and turned it over, you can clearly see the pins for the digital and analog ports.