The CSS Designer is exclusive to Dreamweaver CC. It is not part of Dreamweaver CS6. However, you can download a 30-day trial version of Dreamweaver CC from http://www.adobe.com/go/trydreamweaver/.
The CSS Designer replaces several panels in Dreamweaver CS6. To learn how to use the appropriate panels in CS6 to style web pages, you can follow my six-part written tutorial for building a first website here: http://www.adobe.com/devnet/dreamweaver/articles/first_website_pt1_cs6.html. It uses a different design from the Bayside Beat site in the Dreamweaver CC tutorial, but teaches you all the basic knowledge you need to get up and running with Dreamweaver CS6.