To get to Sydney Central, all you need to do is to buy the train tickets from the airport.
It's pretty convenient - just that it's really expensive (i think it was $18) for a 10 min ride :)
I never felt so old before... Probably i should opt for YHA or some other cheap hotels :)
Then again, we requested until we got ourselves an all-female dorm.
(pretty an experience especially if we are traveling alone)
It's interesting seeing different room mates every night, all over from different countries, and I was surprised how 'quiet' they were during the night. In fact, it was too quiet that they weren't even back home!