Artarmon is on the North Shore of Sydney, approx. 10 km from the city centre.
Take any train from Sydney airport to Central Station (13 min).
Change train to North Shore Line train (Direction Berowra) (23 min).
Get off at Artarmon Station.
7 minute walk or call Christina's taxi service ;-)
Cost $12 per person.
or
Grab a taxi (approx. $55)
Sydney Trip planner: http://www.131500.info/realtime/default.asp
Find an address in Australia: http://www.whereis.com/whereis/home.do