If you click on the network icon in your panel, and select Edit, you get a dialog where you can select your active network connection. Select this and click Edit, then click the IPV4 tab, then you will see a text box where you can set DNS servers as a coma separated list.
I have experimented with Google's DNS servers but have not seen any noticeable difference at my location. However I have added the OpenDNS servers because I find I need these to make GoogleEarth reliable.
Notebook: HP 14 Notebook PC 14-r003TX, i5-4210U @ 1.7 GHz, 8GB RAM, Linux Mint 17.2 (Dual boot with Win 10)
Notebook: DELL latitude E5520, i5-2520M @ 2.50 GHz, 4GB RAM, Linux Mint 17.2