When you install WordPress, depending on how it is done, you may find that your URL is in the form of http://myblog.org.au/wordpress/. To remove the “wordpress/” bit is fairly straightforward.
First, go to your cPanel, and open the File Manager, which should be under “Files”.
Under public_html you will see the wordpress directory. Open the wordpress directory and copy all the directories and files inside it into public_html.
Second, open phpMyAdmin which will be under “Databases” further down cPanel.
On the left you will see _wordpress and _wp1 (this may be called something else depending on how you installed MySQL. Some people advise not calling it “wp” for security reasons). Click on your _wp1 and then on wp_options from the list on the left.
You need to change two of the entries, “option name” sitreurl at the top and home further down at about entry 37. Use the “>” at the top to turn the page. Click the “edit” pencil at the left of the line and remove the “wordpress/”. There is advice online to leave a single trailing “/”, but it does not seem to matter in practice.
You should now find that your basic URL will now bring up your website. Make sure all the links work, including the Home button and the header, which is often also a Home link. The wordpress directory can now be deleted if you wish as it is redundant.
See the official URL change wisdom at http://codex.wordpress.org/Changing_The_Site_URL