We will use the Ubuntu Software Centre for installing Audacity. First open the Ubuntu Software Center through Applications -> Ubuntu Software Center:
Type into the search field 'Audacity' and search results should be returned automatically:
Highlight the Audacity item (it should be highlighted by default) and click 'Install' and you will be asked to authenticate the installation process.
Enter your password and click 'Authenticate'. The installation process will begin.
When the process is completed you get very little feedback from Ubuntu. The progress bar at the top left disappears. The 'In Progress' text on the right also disappears. Audacity should now be installed available in your Applications menu.