The fastest route is probably intercity train from Hung Hom.
Then you have the option of direct buses (more reliable services at China Travel -
http://www.chinatravel1.com ).
Or the even more cheaper way that I use is, cross over to Shenzhen first, then pick a coach at the central coach station just outside the train terminal building. Not much recommanded for foreigners as they don't speak English...
All the bus usually terminates at one of Guangzhou's major hotel - probably White Swan. In any case you'll need to take a taxi from there to the airport...
Air tickets from Guangzhou is *a lot* cheaper than from Hong Kong or Shenzhen... And offering a lot more domestic destinations, in case you are more adventurous...
