Hey, you need a broadband connection. You can connect wireless and wired. I personally prefer wireless becuase my computer can be three rooms away. Just go out and buy a cheap wireless router, run an ethernet line from your router to your modem, go into your Wii's internet set up and follow the directions. Call Nintendo for any help you need, 1800-255-3700...if your in America.
You can find your friend code in the message section as well. It shouldn't be too hard to find it...it's pretty straight forward. My Wii username and friend code is under my Wiichat username.
If you have any other questions, private message me.
To add friends..Get somebody's friend code and go into your messages from the menu. Feel free to add me, I'd be glad to be your friend on there.