Are you taking some time to see the sights in Australia? Are you intending on working in Australia at the same time? If you've got your passport, you may be able to obtain a Work And Holiday Visa (Subclass 462. It is similar, but not the same as the “Working Holiday Visa”) that will permit you to travel in Australia, as well as leave and re-enter the country for up to 12 months. It also grants you the ability to work with a single employer for up to six months, and study for up to four months.
With the stated goal of “encouraging cultural exchange and closer ties between Australia and eligible countries”, it's an excellent option for younger people who want to get out and see the world. As long as you are between the ages of 18 and 31, do not have a child accompanying you, and have a passport from a valid country (such as the United States) you can potentially obtain such a Visa.
Other requirements for obtaining the visa include having sufficient funds to support yourself during your stay. You should have enough money to purchase a return ticket at the end of your journey, meet certain health standards (this may require some doctor's examinations), educational standards (high school diploma), and “character requirements”.
The character requirements, in particular, are rather detailed, you can view them here. As an American citizen, you won't need to provide a “letter of government support” to obtain this visa, but you will still have to meet all of the other requirements, and not have any outstanding debts to the Australian government.
How To Obtain The Visa
As long as you are outside of Australia, you can apply for this temporary visa (make sure you get your visa approved before finalizing your travel plans). You will need to get all of your paperwork in order. A full listing can be viewed here, and it consists of numerous government forms, photographs, birth certificates, and supporting documentation showing that you have enough money for your trip, meet educational requirements, and can speak English.
Citizens of the United States have the ability to apply for an Australia E-Visa, and can submit their required documentations and pay the necessary fees online. The Australia E-Visa system, ImmiAccount, also allows you to track your application status.
Once your Visa is granted, you will be notified as to the specifics of your visa (when you can obtain it, the grant number, conditions), and if your Visa were denied, you'd be informed why and told how long you have for filing an appeal.
Once you are approved, you will have a 12 month period in which you can stay in Australia. Observe all laws, and enjoy yourself while working or studying in the country.