The Wii out of the package connects via WiFi, so if you do not have a wireless router you can use to connect to the internet, you will have to find a different means to connect your Wii to the internet. If you have DSL, you can by an ethernet adapter for the Wii that plugs into the USB ports on the back of the Wii, then plug your DSL line directly into that.

If you have dialup, I am not aware of a way to hook up your Wii to that, has the Wii does not have a dail-out function that would allow it to place the call needed to connect to the internet.