In addition to the suggestions from Tesserax, if you have a current or recent version of the operating system on your Mac, you might want to consider using the option in Apple's setup wizard to "Replace an existing device", which is a process that guides you through the setup and installation of the new AirPort Extreme.
The example below shows an AirPort Express as the the "new" device, but you would see your AirPort Extreme pictured on your screen.
The setup wizard will automatically transfer all of the existing settings from your old AirPort Extreme to the new AirPort Extreme and then reset the old AirPort Extreme back to factory default settings. Once that has been done, it will be a simple task to set up the old AirPort Extreme to "extend" the signal from the new AirPort Extreme using a different wizard setup template.
A possible question here might be how old your "old" AirPort Extreme might be? I'm assuming that you have a "flat or square" version of the AirPort Extreme.....and not the very old "round or dome" shaped AirPort Extreme. It might be a good idea to verify the model number of the old AirPort, to make sure that it would be compatible for this purpose.
Please look on the bottom of the old AirPort to locate the model number. It might be on a label or embedded in the foam pad base. The model number starts with an "A" followed by four numbers. Post back with that model number, please......if you want to consider using Apple's setup "wizard".