How do I update an iPad Air to current software version?

Your iPad Air model may not be able to upgrade/update beyond any version of iOS 12, currently at iOS 12.5.3.

The 2013 iPad Air 1, iPad Mini 2 and 2014 iPad Mini 3 cannot upgrade beyond any version of iOS 12.

Sorry.

These iPad models have overall internal hardware that is too old, too underpowered and incapable of running all of the new, advanced and internal hardware resource intensive features of iPadOS.

These iPad models will soon be 7 and 8-years old, in 2021.

Sorry.

There is one last thing you can try/attempt, if you need older versions of apps.

If you own another much newer iOS device that can run iOS/iPadOS 13 and later, you can install the most recent version app/s onto that more recent iOS device.

Then go back to your older iPad, open the iOS App Store, go to the Purchases section of the store app, search for the app/s you wish to try and download to that older iPad and see if an older version of the app is allowed to be downloaded/installed to that older iPad.

These newer iOS/iPadOS devices must use your same Apple ID user account and password.

Failing that OR IF NO joy, then there is nothing more to be done.

It's 2021, now.

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a purchase of a new iPad model OR a much, MUCH “newer” and less expensive, refurbished or used iPad models, from better known, trusted sources, like other Apple product/device retailers/resellers, some locally or from online, on the Web/Internet, capable of running the latest iPadOS versions.

There are PLENTY of newer, older iPad models that can run the latest, current versions of iPadOS.

I am sorry that you had to learn all of this, but this does not change any of the facts regarding these very old iOS devices.

Sorry & Best of Luck to You!

If it is the original Air model, it cannot be updated beyond iOS 12.x.x.x. It does not have the components needed to run newer software.