You will have to supply an IP configuration of IP address and subnet mask to both the NAS box and the 2nd Gb port on the media server - the IP addresses need to be on the same subnet, obviously.
It would also be necessary to ensure that the new IP subnet is not the same as the one you are using for the 1st Gb port on the media server (existing home network).
If you have console access to the media server, then you do not need to set up routing on the media server, but no other device will be able to reach it.
Otherwise you would need to configure the media server as a router, and configure static routes appropriately on various devices - e.g. a default route on the NAS via the media server and static routes on other devices.
Configuring the NAS could be "interesting", though - as mixture says, RTFM, very carefully!
I assume that the NAS will be wired in its final resting place, and the media server is wireless, yes?
SD