How to view the DNS address assigned by DHCP?

For at least Ubuntu 15.10 onward (possibly also earlier versions) run in a terminal:

nmcli dev show eth0 | grep IP4

eth0 is the most common iface, but it could be eth1, eth2, etc.

For older versions use nmcli dev list iface eth0 | grep IP4.

$ nm-tool 

will also list DNS Servers.

To get the DNS address open terminal (Ctrl+Alt+T) and type:

cat /var/lib/dhcp/dhclient.leases | grep dhcp-server-identifier