First, changing DNS settings is almost the same on all Linux distros, but I just love Ubuntu based distributions. As a second, why changing DNS settings anyway? There is so many reasons for YES and for NO.
The main question is where on Internet resides services you use? Close or far from you? I will discuss about this issue some other time.
Its common to use DNS that your ISP is forcing. But if you like to change you DNS, for instance to Google DNS, procedure is as follows. On desktop, in the upper right corner, pick options button and then option System Settings… (Slide 1.).
In System Settings pick icon Network (Slide 2).
In Network window take Options.. button in bottom right corner (Slide 3.).
In Options… in DNS servers dialog enter IP address of Google DNS servers(126.96.36.199 or 188.8.131.52) (Slide 4.). Of course you can add more then one DNS server record to your settings. When you are finished save your settings and start to use your new DNS settings.
List of public DNS severs you can find here.
I hope that this tutorial was informative to you and thank you for using this website.