How to Restore an iPhone That Hangs on the Apple Screen

When all is well with your iPhone, you won't see the Apple logo screen very often, if at all -- it only shows up when you start up your device after it was fully shut off, or when it restarts after you install an update. The problems start when this screen appears but doesn't disappear -- if it sticks around for longer than 10 minutes, or your iPhone keeps restarting but never gets to the home screen, you might need to restore it from a previous backup to get it to work again.
1 Wait for It
First things first -- if your iPhone seems stuck, but it hasn't yet been 10 minutes, wait. Restoring your iPhone will always mean losing at least part of the data you had on it, unless your last backup is literally just a few minutes before the issue started happening. If your iPhone is well and truly stuck, restoring it is a necessary evil, but you want to be absolutely certain that it is unavoidable before you start.
2 Try Resetting
If your iPhone is frozen on the Apple screen, a reset may help you get it unstuck. Press and hold both the Home and the Sleep / Wake buttons simultaneously until the Apple screen reappears, then release them. This should take approximately 10 seconds. After doing this, wait out the ten minutes and see if your iPhone loads past the Apple screen. If it does, the issue is fixed. If it freezes again, however, or if it was stuck in a continuous restart loop in the first place, you'll need to restore it. To prepare your iPhone for the restore process, press and hold both the Home and the Sleep / Wake buttons simultaneously again -- this time, however, release them as soon as your iPhone switches off, before it can restart.
3 Restore It
Connect your iPhone cable to a USB port on your computer, but not to the iPhone itself, then launch iTunes. Press and hold the "Home" button on your iPhone and connect the cable to it. The device will turn on, and iTunes will prompt you that it has detected an iPhone in recovery mode. Click "OK," click "Restore" and then work through the onscreen prompts to restore your iPhone to the factory settings.
4 Get Your Data Back
Once your iPhone is back to its factory settings, you need to set it up again. Work through the setup screens on the device until you're asked whether you want to set it up as a new iPhone or restore it from a backup. At this point, you can select "Restore From iTunes Backup" or "Restore From iCloud Backup," depending on where your most recent backup is located, to get at least some of your data and settings back.