Instructions
Check it is the three-segment red ring, not the four-segment one. With the "Red Ring of Death," the upper right quadrant of the circle is not illuminated. The four-segment ring indicates an improperly connected AV cable. Check all cables are properly connected before continuing.
Switch the console off and allow it to cool fully before trying to run the console again. If it fails again, try moving it to a different location. There is more dust down at floor level so the 360 may benefit from being up on a table. If it is definitely an overheating problem, then an aftermarket cooling unit can also help prevent this.
Visit the Xbox support website (linked below) and click "Contact Us" from the very bottom of the page. Click the "Call Us" button from the bottom right of the contact page. Dial the number and select "Faults" from the automated menu. You'll be required to answer several security questions, so have to hand your gamertag, your password and the email address associated with your tag.
Having reported your fault, a collection will be arranged. Pack up your box, as per the Microsoft operator's instructions, label it with your details and await collection. Your 360 should return shortly, fully functional again.