Copy the wp-db-backup.php file to /wp-content/plugins/
Activate the plugin at your blog's Admin -> Plugins screen
The plugin will attempt to create a directory /wp-content/backup-*/ inside your WordPress directory.
You may need to make /wp-content writable (at least temporarily) for it to create this directory.
For example:
$ cd /wordpress/
$ chgrp www-data wp-content (where "www-data" is the group your FTP client uses)
$ chmod g+w wp-content