If you want to have a self-hosted Joomla! installation you will first need to go to joomla.org and download the latest release of Joomla! from the website.
In order to share your site the internet you will need a web hosting service. There are many to choose from within Australia and members of our community have made their own recommedations in our forum. A lot of these web hosting companies also have a step-by-step guides in how to install Joomla! within their environments.
Once you have uploaded the package to the web post you will need to unzip the package, create a new database for the website and then go through the quick and easy five minute installation process with Joomla!
There are a few technicalities that you may need some help with, such as pointing your domain name to your web hosting environment, but your web hosting provider should be able to provide assistance in this situation; most may even provide free domain names with hosting packages.