When you apply online at the above website, you enter you passport number and some additional information, then pay the fee. It is a very simple process. You will then receive an email comfirmation within 24 hours. You do not need to print anything out, it is all entered into the Australian immigration system online. Very slick system.

You can print out the confirmation for your own peace of mind, but like the OP said, it is not necessary at all