You can use the Airport Link Sydney train that runs through the city.
Opal Cards are rechargeable smart cards for use on all public transport within Sydney. They are available at the concourses at the Sydney Airport stations. You can also use compatible AMEX, VISA, and Master Cards instead of an Opal Card. If you have absolutely no plan to use public transportation while in Sydney, you can get Opal single tickets for one-time use, although they are comparatively expensive.
Airport Link is this train goes through the "Airport International" international terminal station and "Airport Domestic" domestic terminal station, and enters a loop line that moves around the center of Sydney in a horseshoe shape (counterclockwise).
It goes to the city center via Sydney Central station, Museum station, St James station, Circular Quay station, Wynyard station, and Town Hall station and then loops back to Sydney Central station. If you have a lot of luggage and need a taxi to pick you up, it is best to go to Sydney Central station, Circular Quay station, or Wynyard station.