The router does simplify things, alcove, by not having to switch cables around every time you want to go online with either the PC or the PS2.
Shwen- you don't need to unplug any cable. Use another bit of ethernet cable and run it from one of the outgoing ports on the back of the router to the PS2. Then go through the set up process. You may have to make some setting changes on the router to get the PS2 online (either setting it up in the DMZ or set up a custom IP address for it in DHCP) as well as include several numbers in the PS2's connection save (router IP address, subnet mask, DNS servers, the PS2's IP address if going the DHCP route).
Most of the numbers you will need can be found within the router set up pages on a status or summary page.