Alright...The Jeep is back in business. As promised I took some photos of the old parts and will post the details of the replacement process. First off here is the broken A/C Compressor still installed in the Jeep. You can see the bad pulley on the front of the Compressor which is facing the fan shroud.
To remove the compressor I had to first remove the bolt attaching the A/C hoses. Here is where you need to be ready, because any A/C gases (which are now Ozone friendly) that are in the system will rush out. In my case this wasn't too bad since the Jeep is eight years old and the A/C hasn't been very cool for the last year or two. Next I had to simply remove the four bolts at each corner or the compressor and disconnect the power connector (a simple clip at the rear of the unit). The unit then lifts right out.
The new compressor goes back in the same way the old one came out. Here is a picture of the new unit installed (nice and shiny). I also installed a new serpentine belt since I was still running on the original.