To remove your existing gearknob and gaitor do the following:
First you get hold of the leather gaitor and pull it upwards at a slant which then uclips it from the base (ashtray surround area).
Then you lift the gaitor upwards pulling it over the gear knob, the gaitor will now be inside out.
There is a black plastic base at the bottom of the gear rod, push this upwards gently, and once free all you do is firmly pull the lever upwards, holding a solid part. This will then pull the complete unit off the metal gear rod freeing it from the car.
Now pull the plastic surround gently upwards, this will come out very easily. Turn the surround over and unplug the connector.
Replacing is the opposite but you need to unclip the 'DSG' trim on the gear knob.
When refitting use a small screw driver to push the metal rod within the gear knob head away allowing the black plastic tip on the gear leaver to come in and then when you release the metal rod it will feed into the hole in the black plastic tip allowing the button on you DSG gearknob to operate.
That's how you change the whole unit over, I'm afraid I don't know how to separate the gaitor from the knob but I hope this helps with part of your problem.
Cheers
Kenny