As on other platforms, after installing the Steam application, it will continue to independently update– without the connection to the Ubuntu Software Center, but is still connected to the official Steam for Linux repository.
 
To celebrate the completion of development, Valve launched a promotional sale of Linux compatible games with discounts of up to 80%. The sale, which runs until February 21st, comprises more than 50 titles, the list of which you can see here. Clearly, if you already have some of the Linux-compatible Steam games in your collection; it will be available as soon as you sign in with your Steam Linux client.

Will you be trying Steam on Linux? Let us know in our Forum