I don't see what it is you are asking for here, but I can try to give a generic answer.
The slim PS2 does not have a wireless network card. In order to connect the PS2 to your home network, you have to use an ethernet cable and connect it to a switch or a router.
If you have a wireless router, chances are that it also has sockets for ethernet cables.
If you absolutely want to, you could buy another wireless access point, use a cable to connect it to the PS2, and have that wireless access point be connected to your wireless router. I think that is a very backwards solution though, and I don't see the big idea of using wireless connections for devices you don't move around a lot.
I made a neat visualisation of how it would turn out.
"Wireless-thing" is the wireless access point I mentioned it is a unit that you need to buy. It doesn't care what you connect to it, as long as it's got network support, therefore, you can connect a PS2 to it just as you can connect for example a PC to it. Both options require you to buy a network cable, though the first option would need a shorter cable than the second, but it would also cost a lot more, and be harder to set up.
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