You would need to know what ur web site consist of and thus what should be backed up/restored. Usually sites are composed of files and databases. U must take care of them all if u want to have ur site exactly the way it has been before.
There are two parts to a complete back up of your Joomla site.
1. The database
2. And the other is file system
Instructions on how to backup a database using PhpMyAdmin is here : www.phpmyadmin.net/documentation/#faq6_4

or Alternatively, there are several backup extensions for Joomla 1.5. (though u mentioned here don't want to use a plug-in, however u may use Akeeba Backup utility)
For File Systems. besides the DB, u should also back up ur site files. The interval for this depends on how often u or ur users make changes to the file system. If users can add photos and media or u make changes to the site other than simple text edits, it should be done often.
NOTE: This is best done with an FTP program and is no different than backing up a standard website. Download all the files and folders that exist in the main directory, and save it to a folder on ur local computer. Be sure that the file and directory structure remains the same as it is in the live site. U could then burn a CD or save to an external hard drive if u desire.

CAUTION: Most hosts provide an FTP capability from within their control panel.

Hope this helps u!