Launch AirPort Utility from your Applications:Utilities folder.
Select your device and click the Edit button from the info popup that appears.
Click to select Export Configuration... from the File menu.
Choose a filename and save location for your configuration and click the Save button.
You may now disconnect your original base station and connect the new one. Notice that AirPort Utility will show one Other Wi-Fi Devices at the top left of the window. Click the Other Wi-Fi Devices button and select your new base station.
Follow the wizard to create a basic network on the new device. Enter a password for the new network, click Next, choose whether to send diagnostic information to Apple then click Next, and the click Done.
The base station will now reboot. Once it appears in AirPort Utility again, select it and click the Edit button.
Select Import Configuration from the File menu.
Navigate to the folder you save your previous configuration to, select the configuration, and click the Open button.
You will now be asked which configuration settings you would like to import. Select the ones you want and click OK.
Over look the settings to make sure everything is correct and then click the Update button.
Click the Continue button to confirm.
Once your new AirPort Extreme or Time Capsule has restarted you will be up and running with the same configuration settings as your previous device.