Yes I'm sure a DSL connection will work for the Wii.
If you're Wii is close to your modem and you have a wired router, all you need is a Wii LAN adapter. They cost about $25.
If you don't have a wired router, you will need a wireless router. A Wii has the ability to search the environment around you for any access points (wireless routers).
WiiConnect24 is a service which lets your Wii use all it's special internet features.
If you need any more info, just ask.