After checking in, walk to the International Airport Station(2 minutes). Take the Inner West & South Line, towards City Circle via Museum, and get off at Wynyard Station. The Menzies Sydney hotel is just next to the Wynyard Station. Alternatively you can transfer via Central Station.
Train is the best way to reach it from other places as well.
Please use the link below to check the timetable and other info on the trains: http://www.transportnsw.info/