1. Try doing a hard reset:
Press and hold both the Home button and the Sleep/wake button simultaneously for about 15 seconds and release when the Apple logo appears.
2. If that doesn't solve the issue, backup the device and restore it as new.
In that case, use: http://support.apple.com/kb/HT4137
NB: set up as a NEW device because a software issue will be in the backup. If the issue persists after restoring as new, you should offer the device for service.
If you get specific error messages/codes in iTunes when updating/restoring, check this: http://support.apple.com/kb/ts3694 for causes and solutions