Copy and past the result into a blank page and save.
There are a load more options about if you want to have the database structure or just the data etc. Just give it a go with different settings.
To put the data etc. back just to to the SQL section and cut and past your code into the "Run SQL" box and press go at the bottom of the box.
Thats the simplest way I think; you can get other code which you can have on your server where when you visit a page it will backup you database to a folder on the server.
Features
with a click (or may be on weeklly basis) the database will be backed up
in a text file and emailed to the admin.
restore the file.
admin need to download the text file from his email and go to the admin
page and upload the databse structer and the data in the tables.
i know its very simple to do in PHPMyAdmin as you have mansioned earllyer.
but its not whats on my mind.
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