Q: How to join an Airport Extreme Base Station to a new modem/router?

Thanks for the reply. My Airport Extreme is actually a Time Machine and if I reset it will my existing back ups be safe or will I lose them?

Hi Tesserax - Many thanks for solving this problem. Although I had a slight panic when my old backups did not appear at first!    

One further question:

I was hoping to use my Time Machine to extend my wireless network, but it seems that in order to do this I have to physically link the two routers using a network cable. Is this the only way? Or can I set it up by a physical connection to the modem/router first of all and then disconnect and move the TM to my preferred location?

OK - many thanks for your assistance!

Tried this first but it failed - presumably because both locations are using different mains rings and connect under different rcd's on a split consumer unit.