I have an 2014 MacBook Air using Yosemite. What operating system can I update to and how?

Installing a newer OS is called an upgrade.

Your 2014 MacBook Air can upgrade to any available OS including the latest macOS Big Sur.

I would recommend upgrading to macOS High Sierra first before installing either Mojave, Catalina or Big Sur.

For older OS’s,

Open Safari and click on this link, 

How to get old versions of macOS – Apple Support

Go to the Download OS section and click on the OS you want to install.

If you want to install Big Sur, open Safari and click on the link below.

How to upgrade to macOS Big Sur - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS ******.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.

If you are considering upgrading to Catalina or Big Sur be warned they do not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/ then contact the developers of the software to see

if they are providing 64bit updates or alternatives.