How do I update my iPad Air 1 to iOS 13?

You can’t.

A 2013, 1st gen iPad Air cannot upgrade/update beyond any version of iOS 12.

Its internal hardware is too old, now, too underpowered and completely incompatible with any of the current and future versions of iPadOS.

If you need an iPad that can run the latest and greatest versions of iOS, as well as, the most current apps available, then, you need to purchase a new iPad from Apple or a discounted, refurbished iPad from Apple’s Refurbished & Clearance section of Apple’s Website or a new or refurbished iPad from an Apple authorised, third party retail or online reseller OR other trusted sources for new or used Apple products.

Sorry & Best of Luck to You!

You don't, if it's the first generation iPad Air. Your iPad is now too old and under powered to run iPadOS 13. It's also no longer supported. If you need the newest iPadOS, it's time for a newer iPad.