How to override the DHCP-provided nameserver?

If you want to override or append to the name servers suggested by the DHCP server, you can configure this in /etc/dhcp/dhclient.conf, eg:

interface "eth0" {
    prepend domain-name-servers 10.0.0.2;
}

You can also do this from the "Edit Connections" control in the network indicator in Unity or GNOME.