It's Safe to Download iOS 9.3.2 for iPad Pro (9.7-inch) Now

Apple posted a KnowledgeBase article with several sets of instructions and the following images for those encountering errors:

Turn off your device for 10 seconds. | Disconnect your device for 10 seconds.

The instructions for installing the update OTA:

Update wirelessly or over the air

1. Try to update your iPad.
2. If you see one of the above screens, disconnect the Lightning to USB cable from your iPad. If you're not connected to power, hold down the Sleep/Wake button for one-two seconds, then let go.
3. Wait 10 seconds.
4. Connect the Lightning to USB cable to your iPad, then connect the cable to power.
5. After your iPad turns on, make sure that the date and time are correct. If the time's wrong, set it again.
6. Tap Settings > General > Software Update, then tap Install to complete the update. Keep your device connected to power until the update completes.

There also instructions for running the update through iTunes on a Mac or PC:

Update using iTunes

1. Try to update your iPad.
2. If you see one of the above screens, disconnect your iPad from your computer.
3. Wait 10 seconds.
4. Connect your iPad to your computer again.
5. When you see Unknown Error (9) in iTunes, click OK.
6. Click Update in iTunes to complete the update. Keep your device connected to power until the update completes.

If you have Error 56 on your device, you'll also have to use iTunes:

If you see error 56 and your iPad Pro (9.7-inch) goes into recovery mode

1. Make sure that you have the latest version of iTunes.
2. Connect your iPad to your computer with a Lightning to USB cable.
3. Open iTunes and select your iPad.
4. When you see the option in iTunes to Restore or Update, click Update. iTunes will try to reinstall iOS and restore your iPad without erasing your data.
5. When you see one of the above screens, disconnect the Lightning to USB cable from your iPad.
6. Wait 10 seconds.
7. Connect your iPad to your computer again.
8. When you see Unknown Error (9) in iTunes, click OK.
9. When iTunes asks you to update or restore again, choose Update. Keep your device connected to power until the update completes.
10. If your iPad appears to update, but it stays in recovery mode, you need to choose Restore in iTunes. During a restore, iTunes erases your device and installs the latest iOS software. After you restore your iPad, you can set it up from a backup.

Lastly, Apple noted that some users may need to reset the time on their device:

If the time is wrong after you update

Make sure that you stay connected to the Internet, so your iPad can set the correct time.

If you changed your settings, so you could set the date and time manually, go to Settings > General > Date & Time, then set the time. If you need help, try these steps to set the time.