Fly, its 4000km (2500miles) via road if you go the most direct way
Here are the main Aussie airlines:
www.virginblue.com.au
www.qantas.com.au
www.jetstar.com.au
I have done the train ride its nice but takes about 4 days from memory and a lot of it is through desert which can be a bit boring! Its also very expensive.
I don't know if Buses go from between Sydney and Perth. If you want to see some stuff along the way I would bus or train or both from Sydney to Adelaide via Melbourne then fly from Adelaide to Perth. Sydney to Adelaide is only 1400km.
Dave