Quite close, unusually for a big city the airport's right in the middle. It's a ten minute train ride to the city. You can get a cab and if it's in light traffic it won't cost that much.
The IATA Code for Sydney is SYD.
You can catch a taxi, bus, train or even a limousine. The train takes you to Sydney's central station.
sydney has both a domestic airport and an international one.
If you fly with Qantas, you will land at the airport Berlin-Tegel.