Instructions
Power on your Wii and select "Wii Menu" from the bottom left corner of the Wii menu.
Select "Wii Settings," then select "Internet" from the second page of displayed options.
Select "Connection 1" and choose "Wireless Connection." Note that in order to use a wired connection, you need a special USB dongle sold by Nintendo.
Select "Search for an Access Point" to automatically scan for nearby active Internet connections. When the scan is complete, a list of all nearby wireless connections is displayed. Choose your wireless network from this list.
Enter any necessary connection or security settings when prompted, then click "OK." Select "Save Settings" to bind these wireless settings to your Wii console. You should now be able to use your Wii for online gaming and downloads.