How do I do a hard shutdown to reset my iPhone S4?

Reset ( No Data will be Lost )

Press and hold the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears. Release the Buttons.

Restart / Reset

http://support.apple.com/kb/ht1430

Backing up, Updating and Restoring

http://support.apple.com/kb/HT1414