Hi stevo_s,
Backing up your database on a regular basis is a fantastic idea. Especially before installing new add-ons or updating a site.
In PHPMyAdmin, select your ExpressionEngine database and click “Export”. Make sure all tables are selected and the option for “SQL” is set. You want both the “Structure” and “Data” boxes checked, and I use “Complete Inserts”. Check “Save as File” and don’t use compression.
The most important thing is to test it before you trust it. Do that by importing it into a local install and verifying the data.
Should website be turned off when downloading DB or does it matter?
As long as no new content is being added at the time you backup, it makes no difference.
Cheers,