On the router there's usually 5 ports. One for the internet and the others for the connected devices, not sure of the colored ports you speak of. Just plug the PC and TV into similar ports. You need cat 5, 5e, or 6 cable for the hookup.
With the tv and the PC on you would have to go into the Network Settings on the PC and allow the tv access. It should show up in the Control Panels Network Settings in the Advanced tab. Look for 'Media streaming options and it should be on the list.
Windows media player works fine as a DLNA client but it wouldn't stream mkv's to the tv until I added a codec then it worked great. Also there's PS3 media server and Mezzmo which are two clients for the pc that worked for me, in some ways better than Media player.