First of all, this is all done in the Wii's setting, which you can find from the home page by clicking the little spanner icon in the bottom left/right corner. Then find "Internet" and work from there.
Now, if you have a wireless router then you should just be able to search for an access point, and if the Wii supports the connection type (e.g. WEP, WLAN1, WPA) then it will connect and you can access Wi-Fi. If it doesn't allow the connection type, you either have to change it someone (worked out with your computer or internet provider) or not use your router as a connection.
You can use ethernet as a connection, but you need to buy the Wii LAN Adapter to do so – just connect that to your ethernet and set it up.
Some routers have an AOSS button. You can use this as an option. Just hold in or press (this varies) your AOSS button while your Wii searches for the connection. You'll have to check your router's manual to see if/where your AOSS button exists.

{ 2 comments… read them below or add one }
No you don't need a wire the wii should pick up your wifi
where i live it doesnt pick it upw whatever you do (360 and ps3 do) so if your having problems then sorry your ******
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