Hold down both the power button and the menu button for at least 60 seconds. Don't worry about what the phone is doing, it's sounds like the update has bricked the phone. Thankfully, because you were updating using an official Apple update this isn't permanent.
Once you have held the buttons down for 60 seconds make sure you've installed the latest version of iTunes. Restart your computer and wait until it is loaded, open iTunes and plug in your device using the Apple USB Lightning Cable, Select your device and choose restore.
When restoring, don't choose from a backup (You can do this later, we just need to get your device back to the state it was in when it left the factory i.e. working!)
Let the restore run. Note: when restoring from a bricked state it usually takes three times longer to restore than when doing a normal restore so let it just get on with it (Shouldn't take any longer than 3 hours)
When this is done, set up your device again and log in using your iCloud account.
Once done, check the phone is working. If it isn't there is a hardware fault which maybe resolvable by the Apple Genius Bar so make an appointment. If they can't get it working they will replace it there and then, provided your device is registered to your Apple ID.