Hi there,
When my nano stopped working after a few months of use I had to go Apple's page to request a repair:
http://depot.info.apple.com/ipod/
All you need is the serial number for the player. I had already registered my player with them beforehand.
After explaining the symptoms of the fault, the next day I was sent an e-mail telling me a postage pre-paid box had been shipped to me to allow my nano to be returned to be repaired.
After sending the player away, a couple of days later I was sent another e-mail saying my player has been dispatched back to me. When I received it, I found it was a brand new player
In total it took one week for the problem to be sorted so I found the service to be excellent.