This guide will not go over how to do this for the GTI/Rabbit/Golf but I am told it is under the passenger seat.
First thing to do is figure out what type of radio you need. This thread here has great information on this and it is dependent on the type of radio system you have installed in your car and if you have TMPS: http://forums.vwvortex.com/showthread.php?3546751 It is a little ways down the page by the user darkk.
What I have is the premium sound system without TMPS and without Navi, from what this user said I am compatible with any of them.
Earlier radios may come with only one antenna adapter instead of the two. You will need something like this to resolve that issue: http://www.xm-radio-satellite.com/terk-dual-input-antenna-splitter/
Once you know what you need you can then go track a satellite radio of your choice down. There are two ways I know of without going to the dealer. First is Ebay which is what I did and found one out of an Audi A4. The other option is to swap with someone like in this thread here: http://forums.vwvortex.com/showthread.php?2297413
Now it is time to start switching out your satellite radio tuners. Here is where my Bentley manual said it was: “Satellite Radio (tuner) is located in luggage compartment under right side of rear parcel shelf.” No pictures were given. This did not help me too much other than say it was in the trunk on the right side. But here is a picture for where it actually is in the Jetta/GLI/Bora:
This is in the trunk right side on the top under side.
I suggest you test your radio first before removing the old one and installing the new one. Just disconnect the wires and plug it in the new one. Mine had enough length to do this no problem as you can see here:
After plugged in turn on your radio, it should work!
If it does not, recheck you have the proper satellite tuner for your car and its features. Another reason it may not work if the software for the satellite tuner is not up to date. I sadly do not have anymore information about this but I assume the dealer can help you out.
Removing the satellite radio from the trunk is a bit tricky since the screw heads are on the top side which is very inaccessible as you can see from the picture here:
This article helps a lot with how to remove the old radio safely: http://forums.vwvortex.com/showthread.php?2970678
Temporarily until I had time to remove the radio properly I used double sided foam tape and attached it to the bottom of my old Sirius tuner. This is only temporary and I do not trust it for long term use. You can see it here:
Once I remove the old one properly I will either buy the same type of mount and screws but make sure the screw head is accessible or use a combination of zip ties and foam tape. I have not decided which route I will take at this time.
I removed the Sirius radio now that I have found a buyer for it. I used the method of cutting a notch the screw and backing in out like the guide above. Instead of a hack saw blade they cut it with I used a Dremel which made quick work of the screw.
When reinstalling it I made sure to put the head of the screw on the underside so it was more accessible if I need to replace it at some point.