All travelers to Australia, other than Australian and New Zealand citizens, are required to hold a valid visa to travel to Australia.
Visitors from Andorra, Austria, Belgium, Brunei, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Iceland, Ireland, Italy, Japan, Liechtenstein, Luxembourg, Malaysia, Malta, Monaco, Netherlands, Norway, Poland, Portugal, San Marino, Singapore, South Korea, Spain, Sweden, Switzerland, Taiwan, United Kingdom, USA and Vatican City can apply for an ETA that allows you to visit for up to 3 months per visit in a 12 month period. The visa is free but you need to pay a service fee (A$20) to apply.
Australian ETA -(visa class 601)
There is also an evisitor that is valid for all countries in the European Union. There are few different details for work and business.
Everyone else can apply for a 600 class visa that costs A$130
Please read the rules and regulations carefully, they can be lengthy and confusing. Be warned rules can change from consulate to consulate and can take a lot of time and patience.
Australian Embassies and Consulates
Foreign embassies in Australia