The file to change DNS nameservers in Linux is /etc/resolv.conf:
cat /etc/resolv.conf
For example, if you want to set up Google public DNS, open the file:
sudo nano /etc/resolv.conf
And add the following lines:
nameserver 8.8.8.8
nameserver 8.8.4.4
Save the changes with Ctrl+O and Enter, then Ctrl+X to exit from nano editor.
Restart the network:
sudo /etc/init.d/networking restart
Or, in Network Manager, go to Edit->IPv4 Settings tab, choose Automatic (DHCP) addresses only and add DNS IP addresses.