Even easier:
https://service.xbox.com/servicehome.aspx
If you've got a xbox live account that is. It's all web based. I didn't even register my console until the RROD, basically create the account, register your hardware, and open up a trouble ticket.....then they take it and go.
Assuming no one else has registered the console, it's easier than most things dealing with Msft. They send you a box, you send it in, and a couple weeks later you get a box back. On mine, they just send a whole new console, which was sweet because I had one of the old, louder than crap cd drives.
Hell, you even get a free month of XBox live gold to make up for the time you lose!
~Drego