If you have performed a Hard Reset or a Factory Default Reset, the AirPort Extreme will not show up in the main AirPort Utility window because it has not yet been configured to work on your network
Disconnect the Ethernet cable if it is still connected between your Mac and the AirPort Extreme and make sure that the WiFi is turned on at your Mac
Click on the WiFi menu at the top of the Macs screen
Look for a listing of New AirPort Base Station
Just under that listing, click on AirPort Extreme

When you click on AirPort Extreme, the AirPort Utility setup "wizard" will open up and take a few seconds to analyze the network, then suggest the correct setup for the AirPort Extreme.
Follow the prompts to set up the AirPort Extreme again
Alternately, if you don't want to use WiFi to set up the AirPort Extreme, you must turn off the WiFi on the Mac
Then, connect an Ethernet cable from your Mac to the WAN "O" port on the AirPort Extreme
Open AirPort Utility
Click on the Other WiFi Devices button in the upper left corner of the window
Click on AirPort Extreme and the setup "wizard" will open up, analyze the network, then suggest the correct setup
Follow the prompts to reconfigure the AirPort Extreme
Once the AirPort Extreme has been set up, you can disconnect the Ethernet cable and turn the WiFi back on at your Mac if you want to connect to the AirPort Extreme using WiFi