Requirements to Connect the Wii Console Online with a wired connection in order to connectthe Wii console with a wired connection , You will need the fellowing:

A Wii LAN adaptor.
An active broadband internet connection ,Such as DSL or cable.
A compable Internet service provider (ISP),Some ISPs require a sign-in every time you connect online ,Or are otherwise in compatible , Contact your ISP for more information.
Either a broadband modem or wired router with an available ethernet port.
An ethernet cable.