Train from Hong Kong Airport to Causeway Bay or city of HK?

Do local subway trains and/or buses run from HK Airport to the city of HK or to a tourist district like Causeway Bay? If you take the ferry from the HK Airport to Shekou Port, there is a subway train station called Shekou Port right there. I believe buses also leave from Shekou Port, but it's difficult for an English speaker to figure out the routes. There is probably transportation from HK airport to HK other than taxis, right?