By Road, Adelaide
I took the Firefly bus from Stawell to Adelaide and it was really a comfortable 6hr trip!. The bus was quite new and had lots of leg room. There's a toilet on board and dvds are shown throughoutr the journey.
Firefly Express serves the route Sydney-Melbourne-Adelaide daily. The ticket from Melbourne to Adelaide is e.g. 55 AU$.
While Adelaide has a comprehensive bus and train service, and a tram running from the city to Glenelg, the best way to venture further is via the Premier Stateliner network or the Greyhound buses. These serve all manner of upstate locations, such as Ceduna and Barossa (mentioned elsewhere)
For traveling in Australia is the Greyhound a very good option, good busses and a good time-table. You can buy different buspasses in Australia, when you have a pas you can call free Greyhound for make reservation for a seat. I have make bustrips from 10 till 44 hours, a veeeeeeeeeeeeeeeeeeerrrrrrrrrryyyyyyyyyyyy big country is Australia. The busses have also freight onboard for the places they visit. And in the outback they stop also for the mailboxes beside the road for peoples who living far from the rest of the world.
There are so many ways to get to Adelaide. If time is a problem then you will have to fly. If you are travelling from Melb to drive along the coast is beautiful. It is around 920km but very scenic. From Sydney you can drive via Broken Hill. This lets you experience many different landscapes. It is about 1400km so it takes a while but there are lots of things to see on the way. If you have lots of money then flying is great but try to do at least one overland trip. There is no better way to really get to see Australia than to get out into the tiny country towns and outback areas.
There are trains from Sydney twice a week. There are also bus services. A bus company called 'Wayward buses' runs a good trip from Melb that takes about 3 days and includes the Great Ocean road.