Getting TO Australia is actually very straightforward.  Just get online or go to a reputable travel agent, and book a VERY expensive airline ticket. 
No matter where you're coming from its sure to be a loooooong flight, so the tickets generally cost a fortune. 
But its worth it!  Just save up for a while, and when its time to go don't forget to bring several books.  Its very disorienting to leave from North America, spend about 24 hours in the air, and land 2 days later!

There aren't really any other ways in or out of Australia.  For obvious reasons, overland routes are impossible.  Ferries and freighters take a lot of planning and a very long time, and even then they only service a very limited number of starting points or destinations.  Only try those if you're REALLY dedicated.