Assuming you use the latest versions of both Blender and the script, install it by copying the python script (should have a *.py extension) to the scripts/addons folder (the exact location of this varies with the operating system and the scripts folder location option you chose when you installed in, alternatives include somewhere in appdata, but for me, choosing to use the installation folder, the path is C:\Program Files (x86)\Blender Foundation\Blender\2.62\scripts\addons. Once copied there, activate the script from the User preferences window (choose the addons tab and find "G3D mesh import/export").
As for the version of python, that's linked to your Blender version, not the script version. Blender 2.6x uses Python version 3.2 (noting there's no harm in having multiple versions of Python, as the major versions aren't backwards compatible; I have 2.7 and 3.2 for that purpose). I'm also using the 64 bit version.
Ninja'd. Don't see why switching to 32 bit would make a difference though, 64 bit works for me.