How do I set a static DNS nameserver address on Ubuntu Server?

1: Resolvconf writes its dynamic resolv.conf file at /run/resolvconf/resolv.conf. /etc/resolv.conf is a symbolic link to the latter location. If you want to use a static resolv.conf file, simply replace the /etc/resolv.conf symbolic link with a file. This is currently supported but not recommended.

2: As I understand it, the affected machine is running Ubuntu Server edition. In that case it configures interfaces using the ifup program whose configuration file is /etc/network/interfaces. For interfaces configured via the dhcp method, ifup (normally) uses dhclient from the isc-dhcp-client package. Dhclient receives nameserver information from the DHCP server and its hook script /etc/dhcp/dhclient-enter-hooks.d/resolvconf sends this information to resolvconf which puts it into resolv.conf.

One thing you can do is edit /etc/resolvconf/interface-order such that eth0.dhcp comes before eth0.dhclient. (I assume that the relevant interface is eth0.) If you have the default interface-order you can, for example, just add a line eth0.dhcp before the line eth*.

--- interface-order_ORIG    2012-11-06 10:12:47.630529145 +0100
+++ interface-order 2012-11-06 10:13:16.410529800 +0100
@@ -9,6 +9,7 @@
 hso*
 em+([0-9])?(_+([0-9]))*
 p+([0-9])p+([0-9])?(_+([0-9]))*
+eth0.dhcp
 eth*
 ath*
 wlan*

Then add a dns-nameservers line to the iface eth0 stanza in /etc/network/interfaces with the correct nameserver address.

iface eth0 inet dhcp
    dns-nameservers 1.2.3.4

Because eth0.dhcp comes before eth0.dhclient, the correct nameserver address will be included in resolv.conf before the incorrect one.

Another way to override the unwanted behavior of including the DHCP-server-provided nameserver address is to edit the dhclient hook script. E.g., you can add a line like the following (where 1.2.3.4 is a nameserver address you would like to discard).

--- resolvconf_ORIG 2012-03-29 22:37:14.000000000 +0200
+++ resolvconf  2012-11-05 20:53:33.312681077 +0100
@@ -54,6 +54,7 @@
            fi
            shopt -s nocasematch
            for nameserver in $new_dhcp6_name_servers ; do
+               [ "$nameserver" = "1.2.3.4" ] && continue

Yet another possibility (a slightly crude one, since it's completely static) is to add a nameserver option to /etc/resolvconf/resolv.conf.d/head.

3: Setting DNS nameserver addresses has gotten more complicated because machines are becoming mobile, are getting more and more interfaces and static configuration is gradually being replaced by autoconfiguration.

Simply leverage dhclient (this uses google DNS for example purposes). This is much cleaner than the other answers IMO:

1. Back up /etc/resolv.conf: sudo cp /etc/resolv.conf /etc/resolv.conf.auto

2. Edit /etc/dhcp[3]/dhclient.conf (ubuntu 14.04 omits the 3): sudo vi /etc/dhcp/dhclient.conf

3. If there is a line containing domain-name-servers, write down the IP addresses for future reference.
4. Replace that line with, or add, the following line: For IPv4: prepend domain-name-servers 8.8.8.8, 8.8.4.4; For IPv6: prepend domain-name-servers 2001:4860:4860::8888, 2001:4860:4860::8844;
5. Now release and renew IP: ifdown eth0 && ifup eth0

Now restart any network clients you are using (like chrome or whatnot)