Hi, I have some questions for you also.
1) How does the router assign IP addresses? If it's like most, it's a DHCP server. You'll have to set your Mac up to accept that. Specifically, you'd need to go into System Preferences > Network, and set it up as a configuration there. I'd call it something like "Home - Wireless" and set it as the default location.
2) If it's not DHCP, maybe it's DHCP + fixed address. If you know the address of your router (my guess is that it'd be 192.168.1.something), then you can set up your iBook as DHCP + fixed address, and assign it any number on that subnetwork (i.e. 192.168.1.something besides the router IP). You'll have to avoid the PC's IP too, of course.
When you configure either one of these, make sure that you provide the DNS nameservers. These allow you to find the machines that resolve the address names for the web sites.
I think it'll probably be one of the two above. I'd be really surprised if it was using BOOTP or was totally manual with the protocol.
HTH,
~FifthWheel