You got many ways you can hook up your Wii via online:
The Cheapest Way:
Buy a WiFi usb adaptor from any electronic store, it usually sells for 39.99 (USD), and it's mostly referred to as for use of the DS but in the manual itself states that you can use it.
The Original Way:
Get a Wii adaptor, which is coming soon and hook up all the wiring and stuff.
The Best Way:
Get a Wireless router (good ones cost around 70, you may be able to bargain though.), and once you hook up the Wireless router, you can have your Wii anywhere in your household and be connected, this as well goes for laptops as well as the 360 and the Ps3.