To make a backup of your Joomla 1.5 application you need to download all your Joomla files to your computer and export the database that Joomla uses.
How to download your Joomla files?
To back up the Joomla files to your computer you can use an FTP client to connect to your account. Then navigate to your Joomla application folder and download it to your local computer. You can also check our tutorial on how to configure and use an FTP client.
How to export/backup your Joomla database?
To export/backup your database you can check the how to backup/restore MySQL database tutorial.
You can also check our tutorial on how to create a backup of your site and restore it.