As I said before, you need to check through your router's firmware. You can usually access that at 192.168.1.1. If that doesn't work, check and see where that address is typically for your router. Once there usually looking either through a status page, or list of wireless devices will show what devices are connected and their associated IP addresses.
Outside of that, the only way I know to do it is to use Wii Homebrew, which you are on your own there.