Where do I need to put this export script and how to I need to modify it. To make it show up under File->Export?
You first need to rewrite it using the latest python syntax for python 3.1 and new blender APIs
You can then either load into a text window and press Run Script or load it in through the User Preferences / Addon panel.
Ouch! Is there a site that can help me find the new apis based on the old ones?
I suppose there is no documentation that acutally compares now and then (old and new) so I can find the new apis based on the old ones?
Start reading http://www.blender.org/development/