This video shows how to backup MySQL database using phpMyAdmin. I'm using HostGator shared hosting account for this how to video.
As you can see, I logged in to cPanel and then navigated to Databases section where I can access phpMyAdmin. by clicking the shortcut. Once in the phpMyAdmin, I selected database I want to backup and then clicked Export. That's it. phpMyAdmin generated a SQL file I can save to my PC.