The motherboard:
You obviously need to open your Xbox 360 (bye bye warranty, it's only 3 months anyways who cares), and remove your motherboard from the metal shielding (please be aware of static electricity, it will damage your mobo if you're not careful), we will be soldering to the bottom side of the board, under the audio/video plug.
Each pin is conviently numbered on the board (going across it goes 2, 6, 10, 14... then 4, 8, 12, 16, 20... then 1, 5, 9, 13, 17... then 3, 7, 11, 15...)
Starting on top left, then moving across:
Pins 2, 6, 10, 14, 18, 22, 26, 1, 5, 9, 13, 27 (black) - Ground (they're all connected to each other so it does not matter which ground pin you use.
Pin 4 (green) - Green output (VGA)
Pin 8 (blue) - Blue output (VGA)
Pin 12 (purple) - V-sync (VGA)
Pin 16 (white) - Left (Audio)
Pin 20 (yellow) - VGA Mode select (hook to VGA Pin 11, Monitor_ID)
Pin 3 (Red) - Red (VGA)
Pin 11 (orange) - H-sync (VGA)
Pin 15 (Red) - Right (audio)
OK, solder up all your points (easier said than done, just take your time and triple check that all your connections are correct)
End of part II