I have an iPad Air and want to downgrade to iOS 7. How does this work?

I'm sorry, but Apple does not provide a downgrade path for iOS. Because downgrading is unsupported by Apple we cannot discuss it on these forums.

You may leave comments at Apple Feedback.

Nothing. There is no supported method to downgrade iOS versions.

If you are having issues with iOS 8 and you have not done so, you may want to try these troubleshooting steps to attempt to resolve said issues:

• A Reset may cure some bugs. Hold down the Home and sleep/power buttons until the apple logo shows up.

  If still not resolved:

• Reste al Settings. Go to Settings->General->Reset->Reset All Settings

  If its still not resolved:

• Restore the device as new.
  Use iTunes to restore your iOS device to factory settings

Since you can't go backwards to an earlier iOS ... what you should do is reset your iPad to factory default by your iTunes program. Don't forget to do your backups!

Choosing an iOS Backup Method (Should I Use iTunes or iCloud to back up ...)

https://support.apple.com/kb/HT5262

Back up and Restore your iOS Device with iCloud or iTunes

http://support.apple.com/kb/ht1766

iTunes: About iOS Backups

http://support.apple.com/kb/ht4946

Create and Delete iPhone, iPad and iPod Touch Backups in iTunes

http://support.apple.com/kb/ht4946

iOS: Troubleshooting Encrypted Backups

http://support.apple.com/kb/TS5162

Use iTunes to Restore your iOS Device to Factory Settings

http://support.apple.com/kb/ht1414

No, you are not able (i.e., not technically able) to go to an earlier system. What it will do, when you use the iTunes program to do it, is do a "clean install" to the present iOS (which is 8.1) and therefore get rid of all your garbage files and corrupted files inside your system folder. It will be in like condition to coming straight out of the factory door!

It will not bring back iOS 7. As said there is no way to get iOS 7 back. It will simply refresh the iOS 8 installation. This usually fixes bugs or issues with the OS that may have occurred during installation by installing new copies of all the OS files.