Step 1) Login to cPanel.
Step 2) Click on phpMyAdmin in the Databases box.
Step 3) Click on the database you want to backup.
Step 4) Click the Export tab at the top.
Step 5) Make sure "Quick" is slelected.
Step 6) Make sure SQL is selected.
Step 7) Click on Go an you will be prompted to save the database to your computer.
Looking to restore your backed up database, look here.