Fortunately, I was right: The iPhone troubleshooting section of Apple's main iPhone support site contains a walkthrough for situations like this, complete with instructions on how to restart the phone, force quit a frozen app or reset the phone in cases like mine where it has completely locked up. Here are these steps in a nutshell:
- Restart your iPhone: Most people probably already know how to do this, but just in case, you can simply hold the sleep/wake button on the top for a few seconds to bring up a red slider at the top of the display which allows you to power off the phone.
- Quit a frozen iPhone app: I know it's a crazy thought, but it is entirely possible that Apple's wondrous iPhone apps can lock up from time to time. In this case, simply hold the Home button when in the app for about 6 seconds to kill the app. You should be able to jump back into the app without restarting the phone itself.
- Reset your iPhone: Note that this is not Restoring your iPhone; that's the button in iTunes that wipes the iPhone and all your information on it. Resetting an iPhone is nothing more than a hard reset or a forced reboot - you're simply cutting the power and making it reboot. To do this, hold the sleep/wake button and Home buttons simultaneously for a few seconds; the display will quickly wipe itself and you should see the black background and white Apple logo, signifying a reset well done.