This question has been answered in another thread, but since your new, here's the answer:
To connect Wii to the internet you can either
a. buy a wireless router, which will then connect wii to the internet wirelessly
b. just use a plain old non-wireless router and connect Wii to it via a USB/ethernet cable
c. connect Wii directly to your modem, which isn't a good idea if you want your PC to be online aswell
d. get the DS USB internet adapter thing or wait for Nintendo to release the official Wii adapter, that you simply plug-in to a USB port on your PC, which then creates a wireless signal which the Wii can use to get online, but you're PC must be on for this
Hope that helped.