How do I get iOS 16 on my iPad Air 2nd generation?

iOS/iPadOS16 has been announced at Apple’s WWDC - but will not be released as a production version until much later this year; historically, Apple tends to release the “next” major version around September.

At present, the first beta release is only available to registered Developers.

The first public beta versions are not expected to be available for many weeks. Even when publicly released, you should expect to encounter significant bugs and unfinished features; Apple recommended that beta releases are not installed on your primary devices - as data may be lost and/or files created are not guaranteed to be compatible with future or current production releases of the Operating System.

This article from iMore outlines published iPad compatibility by model:

https://www.imore.com/my-ipad-compatible-ipados-16

That version has not been released to the public - you will need to wait.

when it is released it will not support the ipad air 2g though only air 3g