US passport holders must have a valid ETA to visit Australia for up to 3 months. The Australian ETA for US nationals is an online travel authorization that replaces the need for a visa.
The ETA covers vacations, business trips, and transit through Australia. It is valid for a year and allows multiple visits of up to 3 months.
However, if a citizen of the United States wishes to stay in Australia for longer than 3 consecutive months, or for other purposes than those permitted with an ETA, they will be required to apply for an Australian visa for Americans.
This must be obtained from the nearest Australian government diplomatic office in the United States, by making an embassy appointment well in advance of the intended travel dates.
An embassy visa for Australia for US citizens may be issued for purposes of studying, to work, or for residency, among other options. The type of Australian visa issued depends on the needs of the individual American applicant.