Internet Connection Sharing?

[977]

ok, I have 2 systems.
System A runs Windows 7 and has a Wireless card, KILLER Xeno networking card, and a network card on the mother board (nVidia I think). So basically 1 wireless and 2 Ethernet ports in the back

System B is much older (floppy disk era), runs Windows XP and only has one ethernet port for networking.

Is there any way I can share SYSTEM A's WIRELESS internet connection by running an Ethernet cable between the two systems (basically using system A as a router) or do I need to connect one of them directly to the wireless router?
While viewing my network connections, my wireless network connection is listed as "shared" but the local area connection (the ethernet cable between A and B) is listed as "unidentified." Do I need to fix this? Do I need to do anything on system B or just plug it in to system A?