How do I format an Airport device that I wish to dispose of?

You would simply set up the Time Capsule again, just like you did the first time when the Time Capsule was new.

Perform a Hard Reset on the Time Capsule

Connect an Ethernet cable from one of the LAN <--> Ethernet ports on your modem/router (there are probably 4 of them, choose any one that you wish) to the WAN "O" port on the Time Capsule

Click on the WiFi menu at the top of your Mac's screen and look for a setting of New AirPort Time Capsule or New AirPort Base Station

Click on the name of the device just below that listing

When you click on AirPort Time Capsule, that will start up the AirPort Utility set up "wizard". The utility will take a few seconds to analyze the network and then display a screen that looks similar to the example below except that you will see a Time Capsule pictured on your screen.

Network Name......Type in something simple for the temporary network

Base Station Name......Do the same for the temporary device name

Password.......Type in any 8 character password that you want

Verify......Do the same to confirm

Click Next

The wizard will set up everything for you.

Now you can use AirPort Utility to access the settings on the Time Capsule so that you can erase the Time Capsule hard drive. The instructions for that are already posted above

When the erase is done, perform a Hard Reset on the Time Capsule again to erase the temporary network settings that you used to erase the disk.

How do I format an airport?

The AirPort (Time Capsule) must be temporarily set up again to work with your network. Use any device name and network name and password(s) that you want.

Then, once the AirPort Time Capsule is set up, you can use AirPort Utility on your Mac to securely erase the hard drive on the Time Capsule.

Open AirPort Utility

Click on the AirPort Time Capsule

Click Edit in the small window that appears

Click the Disks tab at the top of the next window

Click Erase Disk

Do not use the default Quick Erase setting which appears, because it is not secure. Instead, click the selection box arrows to choose the Zero Out Data option for a secure erase.

Click Erase

The process will take 3-5 hours on average depending on the size of the AirPort Time Capsule hard drive. The Time Capsule indictor light will likely blink amber during the process.

When the erase process has completed, you can now perform a Hard Reset on the AirPort Time Capsule to erase the temporary network settings that were used to allow the AirPort Time Capsule to be erased by AirPort Utility

Now, it is safe to dispose of the Time Capsule.