I've had the Wii since launch and I couldn't even tell you how the Wii works online because:

A) It's a bitch to set up.

B) It's confusing as fuck once you do.

C) There's nothing to do with it online once you have. Unless you want to have a Mii Parade.

^What do you mean by set up online?

I got a Wii this Christmas too... but it had wireless and the online set-up took seconds. All I did was update the firmware.

Unless by online you mean something else.

setting it up online is easy as pie

just go into the settings anf follow the instructions, I think new Wii's even come pre-loaded with an instructional video

Four Words: Nintendo Wi-Fi USB Connector.

Gosh it's such a piece of shit. I hate Vista. I hate wireless.

If you have wireless, it sets itself up pretty easily, if I recall correctly.
And there is more than just the Mii Parade on-line.
You can surf the net, vote, check news and weather.
You can buy DL games on-line. And
for some games, there is a good on-line (where the codes come in).

Mike from Morgantown

May I recommend some good Wii online games?

Get New Super Mario Bros. Wii and Mario Kart Wii.

If you have wireless router, it should take only a few seconds to set it to online. Just go to settings -> internet -> search for an accesspoint and after you find it, enter the password (if any) and there you go.

Friend codes are needed if you want to connect to your friends. You don't need them if you want to play online "with anyone" or use other internet features.
And, there's lots of fun stuff online with Wii, internet browser is handy just like news and weather channels and Nintendo channel is good for trailers and videos about games and stuff like that. And WiiWare and Virtual Console are available through internet.

@Snesboy: Oh USB-Connector and Windows. I can feel your pain.
The problem isn't really the USB-Connector, but Windows and firewall updates that constantly break the compatibility. The connector itself works great. Get a wireless router, that will fix your problems and doesn't cost much.

I got a Wii LAN adaptor and a 25 foot ethernet cable and it's working great.

The Wii lan adapter is the way to go if you can. It gives you the best online experience as you'll notice much better ping times.

I highly suggest you set the online up and check the VC + WW out and grab some games.

@Snesboy: I tend to suggest wireless, since it's useable in other devices too.