The database_backup.sh script should have the following info :
mysqldump -u database_username -pdatabase_password database_name > $PATH
Run the script that performs the backup job.
Using Cron :
Set this script up to run every night, etc. as a cron job. It will save an sql dump of your database every night in the mysql_backup.
* 23 * * * your_userid /path/to/backup/script