The best thing is to just backup your whole harddrive.
If you want additional backups of just your database(s), it is useful to know their location in the file system. As mentioned ealier, you can just right click on a database and choose Show in Finder. Doesn’t this work for you?
Either way… In the Getting Started chapter of the manual, under A Word About Backups:
As a secondary backup option, you can create an optimized and compressed copy of the whole database that you can then save on a server or other media. Use File > Export > Database Archive or Scripts > Export > Daily Backup Archive to create a ZIP file of the database. The former option allows you to choose specific place; the latter creates it in a Backup folder in your home folder.
You could also use the File > Export option. The only difference is that the script names the zip archive and place it in a predefined location.
But I don’t understand why you have a problem with the script. Something strange is going on. When I open it in Script Editor, I indeed see this line:
set this_archive to "~/Backup/" & this_name & " " & this_date & ".dtBase2.zip"
So why would it create the zip archive in your Application Support folder?
I don’t have it set up to run automatically, but if you search the forum or the manual, there is surely a way to automate running this script.
There is already a long thread on backups here – with discussion on that, plus many other things: