Taken from ED38 regarding the front badge:
should be able to tug it straight out by getting your fingers in the gaps in the vw roundell.
If not it's grill off and popped out from the rear, clips are easy....flat blade scewdriver and push the bottom tabs up and pull and top clips push down and pull.
Taken from Club GTI regarding the rear badge:
use a hair dryer...once warm, it should peel off. The badges are generally fixed by an adhesive stip.