In this instance I want to use mysqldump to backup a database using a nightly script.
For this example assume the following;
mysql server host: myserver.example.org
target database: mydb
Backup host: backup.example.org
Backup username: backup
On the mysql server log in as root with;
mysql -u root -p
Enter this on the mysql console;
GRANT SELECT,LOCK TABLES ON mydb.* TO backup@backup.example.org
flush privileges;
On the backup server run this command;
mysqldump --host=myserver -u backup mydb > test.sql
Assuming that works, you can put the final command into your backup shell script or simply place it in your crontab.