I don't know about your router IP - I guess your manual will tell you the default IP address...
What psyno said about DHCP is correct - you can assign your NIC IP from the router itself. I know how to do that in RedHat - run:
from the console (as root), and set eth0 to DHCP mode. Of course, this is assuming you're connecting to the router using eth0
I *think* you can also set eth0 to DHCP mode using:
in a console.
redhat-network-config also allows you to set the IP address manually, or you can edit:
service network restart
to apply changes