At this point, you will need to perform a Hard Reset on the AirPort base station to get it back to its original default settings and then set it up again.
To perform a Hard Reset, make sure that the AirPort is powered up for a minute or two, then hold in the reset button on the back of the AirPort for 7-8 seconds, then release. Allow a full minute for the AirPort to restart back to a slow, blinking amber light status again.
Click the WiFi menu at the top of the Mac's screen and look for a listing of New AirPort Base Station
Just under that listing, click directly on the AirPort base station. The example below displays an AirPort Extreme as the new base station, but you will see your AirPort device on your screen.

When you click on the AirPort base station, the setup "wizard" will open up automatically and take a few seconds to analyze the network, then suggest the correct setup for the AirPort. Follow the prompts.
If you need more help, we need to know which AirPort model that you have, and whether the AirPort connects to your network using a wireless or wired Ethernet cable connection. The make and model number of the device to which the AirPort will connect would be very helpful to know as well. A serial number is not needed, just the make and model number.