You need a router (Wireless Connection) or a LAN Adapter (Wired Connection). Then go to the Wii's Settings Menu and go to the connection area. There you can search for a connection point or enter a connection manually.
That was a very brief overview so if you need further help, just ask.
I have seen the offical lan adapters for the wii but are the 3rd party one good as well because in the Nintendo manual it says 3rd party's lan adpters will not work well something like that.