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 you get specific error messages/codes in iTunes when updating/restoring, check this: http://support.apple.com/kb/ts3694 for causes and solutions
If you're not able to restore the device the normal way, you should use: http://support.apple.com/kb/HT1808
Using that last article will erase everything on the device, so make sure you have a backup!
NB: If you're not able to restore the device with that last article, not even on another computer, it probably needs hardware repair.
Good luck 🙂
Stijn