How do I get google chrome on my new MacBook Air laptop

You can try and download google chrome from googles official site.

If you have tried that and it is not working, what is the exact error that you’re getting ?

is there a problem with the googlechrome.dmg file? won't run or you can't download it?

Take the hint. There is no reason to install Chrome on a Mac. Installing it obviates most of the reasons for having a Mac.