Citizens from several countries can obtain tourist visas, or Electronic Travel Authorities (ETAs), over the internet. These visas are free of charge and are issued automatically. They enable tourists to stay for up to 3 months and can be extended once you are in Australia. Tourists are not entitled to work in Australia.
For citizens of countries that are not covered by ETA arrangements some quite different processes are in place - particularly where the citizen is from a country regarded by the Department of Immigration and Citizenship as being of high risk of non-compliance with visa conditions. If you are affected by this you should contact a Registered Migration Agent for further advice.