Installing the Modchip
Detailed installation instructions and pictures for the Xecuter 3 CE modchip can be found in this PDF document.
Figure 1: Xecuter 3 CE Modchip Wiring
A note to owners of Xbox version 1.0 or 1.6: Version 1.0 of the Xbox will probably have the holes the pinheader is meant to go in filled with solder. Unless you're lucky enough to have a solder sucker, these can be a pain to clear with a solder wick. Have a friend heat the filled solder junction while you gently push the pin on the pinheader through. Version 1.6 of the Xbox requires a special PCB supplied by Xecuter.
Figure 2: Xecuter 3 CE Modchip Installed
Flashing the BIOS
Unfortunately, due to some questions regarding the legality of some of the code in "homebrew" BIOSes, they're not available for easy download from a website. Most of the homebrew BIOSes are listed here. Details on obtaining one of these BIOSes and compiled builds of XBMC can be found here or you can find XBMC builds around the web as BitTorrents. For this mod I'm using the X3 BIOS since it's already a 1024 KB BIOS (saving you the need to pad a 512 KB BIOS to 1024 KB) and it's designed for the Xecuter line of modchips.
Instructions for flashing the BIOS via HTTP can be found here. If you installed the external bank selector, make sure that banks 1 and 2 are selected and that flash protection is disabled. You don't need to worry about this if you didn't install the bank selector, the Xecuter modchip defaults to bank 1 and 2 without it.