We always hear about how Columbus ran into America on his way to India, but never about how Australia was discovered. Was it actually found like Columbus, or was it something that people just sort of knew about?
If you're asking how Australia was discovered by indigenous Australians, I have an answer here.
If you're asking how Australia was discovered by Europeans and Asians, you'll want this answer instead.
This might be a better question for /r/AskAnthropology since Australia was first settled by people between 42,000 and 48,000 years ago.