You need a wired router or a wireless router.
Choose one of these in order of ease/low maintenance/reliability:
- USB wired ethernet adapter (by Nintendo for the Wii) to connect to your wired router.
- Wireless conection (built-in feature of the Wii) to connect to your wireless router. You may have to make sure your wireless router's SSID (network name) is not hidden.
- Wireless USB Adapter, a tiny white USB dongle made for a PC to replace the purchase of a wireless router comes with instructions.