Desktop Client for Google+ and Hangout
There is currently no desktop native app for Google Hangouts. As far as I am aware all usage for Google Hangouts is done through a web browser.
How to install Google Hangout:
Go to the Google+ Hangouts page and click in the Download Plugin button.
Then you will see a list containing options with binary files, this page will read your system information and select automatically the best option for you. Click in the Download Link button and save the file in your computer.
When the download is complete, open the file (double click over it).
It will be open with the software-center, click in the Install button. If it request for your password, enter it.
The installation will start there and, in the Progress label you will see a progress bar.
After a seconds the install will end and you will see the status of this applications as Installed.
Now, in the previously visited download page, you will see that it's installed on your system and you can start to use Google+ Hangouts!
The instructions listed are good, but if what you are looking for is the desktop version of Hangouts, then I recommend installing the Google Chrome extension. Go to http://www.google.com/hangouts/ and click the "Available for your computer" link at the bottom. Despite being a Chrome extension, it makes Hangouts live in their own windows outside of the browser.