For the sake of clarity, this is no different from choosing to explicitly set up any other dns server - instructions here are heavily modified from the google public dns FAQ. It may vary on your DE if you're using a derivative, but network manager is common enough, and your experience should be similar to this.

• In the System menu, click Preferences, then click Network Connections.


• Select the connection for which you want to configure Google Public DNS. For example:


• To change the settings for an connection, select the connection type, then select your network interface in the list. Here, it is called Wired Connection 1. If its a wireless connection select the appropriate AP

• Click Edit, and in the window that appears, select the IPv4 Settings


• If the selected method is Automatic (DHCP), open the dropdown and select Automatic (DHCP) addresses only instead. If the method is set to something else, do not change it.
  In the DNS servers field, enter the IP addresses you want to use, separated by a space:
  
  199.85.126.20 199.85.127.20

click Apply to save the change. If you are prompted for a password or confirmation, type the password or provide confirmation.

• check if you're using the right dns server with their test page