Instructions
Log on to the website xbox.com.
Mouse over 'Support' and select 'Check My Repair Status' from the drop-down menu.
Choose 'Request a Repair' and click 'Start a repair request.'
Sign in using your Windows Live account, or create one if you haven't done so already.
Select 'Add a product' if your console is not already registered. You will need the serial number from the back of your Xbox. Make sure to update your contact information once you have registered your Xbox.
Select the Xbox you wish to be repaired, and choose 'Request a Repair.' If the Xbox is still within the one-year warranty (three years for Ring of Death failures), Microsoft will repair or replace your Xbox for free. Otherwise, you may have to pay a fee.
Place your Xbox in the packaging that Microsoft sends you in the mail. Pack it up, tape the box and place it in the mail. Make sure to take the out hard drive and any discs in your Xbox.
Once in the mail, the repair process should take 2-3 weeks.