I try to download macOS Catalina on my MacBook Air however it somehow doesn’t work. Is there anything I can do to fix this?

Is it a 2012 or later model? See that and other information in How to upgrade to macOS Catalina - Apple Support

What doesn't work and what message do you get when you try?

It could be that you icloud storage is full or do you have a SD card in your mac because you need one for updates

If you are running any anti-virus programs, that can cause it.

If not, create a new Admin user and try again.

It also may be a problem with your hard drive.