This attack is exactly the same as the default gateway redirection, but instead of sending back a bogus default gateway the rouge DHCP sends back a bogus DNS server. This then allows the attacker to quietly redirect just certain requests. For example, you think your accessing your bank WWW site, but the attacker is using their own DNS server to redirect you to a fake WWW site that they have set to capture your details.
Mitigation
The mitigation strategy is exactly the same as for the default gateway redirect. Stop rogue DHCP responses getting onto your network, and you won't get your details stolen by this attack.