I hear that the process is a whole lot faster in the states, like Kave said, but over here, in the UK, you're looking at around 2-3 weeks. Then again there's people on the official Xbox 360 Forums moaning about having to have to wait 5-6 weeks for a refurbished unit to be returned.
If you've got the 3 red ring of death then you should be covered by the additional 3 year warranty. Give Xbox 360 tech support a call (the phone number is here:
Xbox.com | Support) and they'll ask you to box up your 360 and wait for a guy from UPS to come and pick it up and ship it off to Microsoft. They collected mine about a week ago and, to be honest, I've heard so many horror stories of people receiving broken refurbished Xbox 360s -- after almost two months of waiting -- and having to send them off again that I'm tempted to just buy an Xbox 360 Elite.
Good luck either way, though. Let me know how you get on and hopefully it won't take all that long for you to get yours repaired.