Follow the steps in this Apple Knowledge Base article to transfer your purchases and backup your iPhone.

Entering DFU Mode on iPhone, iPad or iPod touch

1. Plug your device into your computer with a USB cable.
2. Turn off the device.
3. Hold the Power button for 3 seconds.
4. Hold the Home and Power buttons for 10 seconds.
5. Release the Power button but keep holding the Home button.
6. After about 15 seconds you will be alerted by iTunes saying that it has detected a device in Recovery Mode.

Make sure the device screen is blank and no logos are present

Exiting DFU Mode on iPhone, iPad or iPod touch

1. Hold the Home and Power buttons until the Apple Logo appears.

Entering DFU Mode on Apple TV

1. Plug the device into your computer using a microUSB cable.
2. Force the device to reboot by holding down the “Menu” and “Down” buttons simultaneously for 6-7 seconds.
3. Press “Menu” and “Play” simultaneously right after reboot, until a message pops up in iTunes, saying that it has detected an Apple TV in Recovery Mode.

Exiting DFU Mode on Apple TV

1. Hold down the “Menu” and “Down” buttons. The Apple TV will reboot.

Press the restore button and allow the phone to complete the restoration data. After it is done, select setup as a new phone.

Next, you can restore the phone again in the normal fashion (not DFU mode) using the most recent backup rather than setting up as a new phone. However, this may cause the original problem to return in some cases. If the problem returns, follow steps 1-3 again and do not restore your backup.