See instructions in: How to download and install macOS - Apple Support
The model year of a MacBook Air is available at Apple menu > About This Mac.
A late 2010 through mid 2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version.
A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later
A mid 2013 and early 2014 MacBook Air can be upgraded to the latest version of Big Sur macOS 11 but no later.
An early 2015 and a 2017 MacBook Air can be upgraded to the latest version of Monterey macOS 12 but no later.
For all of the above, see instructions in: How to download and install macOS - Apple Support
A 2018 or later MacBook Air can be upgraded to the current version of Sonoma macOS 14. See: How to upgrade to macOS Sonoma - Apple Support
Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/
or
https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html