May I suggest this website: http://travel.state.gov/australia.html, under "Entry Requirements":

"Americans may enter with an Australian visa or, if eligible, through Electronic Travel Authority (ETA). The ETA, which replaces a visa and allows a stay of up to three months, is free of charge and is available from airlines and many travel agents in the United States."

I used the above method to obtain my ETA through United Airlines last July. Things may have changed since then and I do apologize in advance if that makes my posting appear to be "misleading" or that it contains "bad info". I can assure you that it wasn't intentional.