How to go 坎培拉 (Canberra) from sydney?most fast and cheap

You can consider taking Greyhound Australia. I know they recently have a promotion on one-way ticket from Sydney to Canberra for AUD15. The total travelling time is about 3.5hrs. It operates from Sydney central bus station to Canberra.

As Canberra is the capital of Australia, the things for sight-seeing would be parliament house or museum.

http://www.greyhound.com.au

the easiest and cheapest way is to join a day tour from Sydney china town. If you want to go by yourself, take the Murray's coach. About $37 one way. Grey hound is not a big company in Australia, and their bus is not as comfortable as Murray, tough the fare is about the same, but the travel time take longer. The cheap promotion tickets you have to buy 1 month in advance. But I think 7 days in advance you will still have a discount. Give them a call.