In Windows, it is possible to get an IP address through DHCP, but force the NIC to use another DNS server that isn't pushed out through DHCP.

I am currently getting a wireless signal on my Ubuntu box. It's complicated, but basically I have to get it through a DHCP server that I have no control of. The DHCP server assigns me an ip address and its own DNS server. I have tried changing /etc/resolv.conf to point to my own local DNS, but the DHCP will change it back. I suspect that I have to add some kind of option under /etc/networking/interfaces in ubuntu, but I am not familiar with the options. Also, is there a way to force a domain name? Again, if I add my own local domain name in /etc/resolv.conf, it gets changed back by DHCP.

man interfaces?

You can use the -R switch with dhcpcd (other dhcp clients must also have something like this), which forbids DHCP to change the DNS settings (e.g. to change the /etc/resolv.conf file).