What you do with the GMOS adapter is splice it to the new head unit's harness. For the most part, the colors will match. When you do it this way, you'll be using the OEM speaker wiring, which will save you hours of time running wires to the different speakers.
Take your time, check off on the wiring diagrams which wire you've hooked up, and for gawd's sakes, use a soldering iron and heat shrink and not butt splices.
One note: do not hook up either the mute or amplifier turn on wires to the GMOS. If you use the GMOS adapter, it will run your audio output through the OEM amp if equipped. That's already switched through the ignition switch.