From cPanel:
First go to your cPanel
Scroll down to Databases
Click on phpMyAdmin link
Select the database you want to backup
Click on the Export tab at the top
Click on the Go button bottom right corner
and save it to your local hard drive
That should do it.
From SSH:
Backup MySQL Database Shell Command
mysqldump -u username -p password databasename > databasefile.sql : Backup MySQL database to databasefile.sql
Restore MySQL Database Shell Command
mysql -u username -p password databasename < databasefile.sql : Restores a MySQL database from databasefile.sql
