Database
Instructions on how to backup a database using PhpMyAdmin (common on most web hosts): http://www.phpmyadmin.net/documentation/#faq6_4
Alternatively, there are several backup extensions for Joomla 1.5 you could look into, JoomlaPack for a full backup of your site or SQL Dumper that can be used for both creating and restoring Joomla databases, Although if for some reason Joomla becomes impossible to log into, the backup will need to be restored through PhpMyAdmin or another method. both these extensions and more are available at http://extensions.joomla.org/
It is recommended to back up the database at least twice per week or even everyday (and more) if you have an active site.