Edit the file
vim /etc/dhcp/dhclient.conf
Uncomment the line starting with #prepend domain-name-servers and set your dns servers. Below is an example using the Google Public DNS.
prepend domain-name-servers 8.8.8.8, 8.8.4.4;
(Note removal of hash sign at beginning and two comma-separated DNS servers.)
Reboot and you should be set. You can verify the servers in use by running
dig google.com
The IP for the DNS server will be at the bottom of the output, like this:
;; SERVER: 8.8.4.4#53(8.8.4.4)