Step 1. Hold and Press Home & Power button for 10 seconds to reboot your iPhone. If it still stuck on Apple logo, you will need to put it in recovery mode.
Step 2. Plug the iPhone to your computer via the USB cable and make sure that the latest iTunes is installed.
Step 3. Press and hold Home & Power button for 10 seconds. Then release the power button but keep pressing the home button.
Step 4. You will see the Connect to iTunes screen and you can let go of the Home button.
Step 5. Now you can restore your iPhone with iTunes.
Resource from: Common iOS 9 Updating Problems with Solutions
I have an iPad Air and iPhone 6, and I tried to update my iPad firstly to iOS 9. It stuck on Apple Logo about 5 minutes during the process! I googled, and found this post which tells 12 iOS 9 updating problems. Hope it works for you too!