Connect a computer to the router with an ethernet cable.
See the literature which came with your router for how to access the user setup screens in the router. Once in go to wireless security and review or renew the wireless security type and password. WPA PSK TKIP is the most common security type in use though some games machine so far only support the older WEP. Make a note of the SSID or change it to one of your invention.
Go to wireless mode and ensure that it's set to a protocol matching your computer and your Wii's wireless mode (mixed mode is a safe bet).
Disconnect ethernet cable.
Go to the computer's wireless networking setup screen and see if you can detect the router's SSID (wireless call sign). Select that network. Ditto the Wii.
Apply the wireless security type and password to the computer's wireless networking setup screen. Ditto the Wii.