If this is a desktop edition, you'd have to use network-manager to check your DNS servers. This can be done by clicking the network icon in the taskbar(bottom right) (if on wifi, it has a wifi symbol, if on ethernet it has a plug-like symbol) and selecting edit connections. Then double-click on your connection and proceed to IPv4 settings. Here, you can add the 8.8.8.8 DNS server. When adding DNS servers, however, I'd recommend you also change the dropdown box which says DHCP to DHCP for address only, so the DHCP doesn't supply you with a DNS server as well. (If you want to do this, you'll also need a router IP, which can be obtained by typing route -4 -n at commandline. It will give output like this:
Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
0.0.0.0 10.0.0.2 0.0.0.0 UG 6 0 0 home
10.0.0.0 0.0.0.0 255.0.0.0 U 0 0 0 home
127.0.0.0 0.0.0.0 255.0.0.0 U 0 0 0 lo
Simply use the Gateway value as your router.
If it's a server edition, you can follow @Kasper's instructions:
sudo echo "nameserver 8.8.8.8" > /etc/resolv.conf
or manually edit the resolv.conf file and put in the dns server
you'd like use.