Open the app in which you want to enter the question mark, then tap the text field in which you want to post the question mark to bring up the keyboard. It's in the lower-left corner of the keyboard. This will change the keyboard's text to numbers and basic symbols. You'll find this icon in the bottom row of keys. A pop-up menu with an upside-down question mark in it will appear after a brief moment. Do this lightly, as pressing and holding too hard will activate 3D Touch, not the alternative keys menu. Without removing your finger from the screen, slide your finger over to the upside-down question mark to select it. You should see the inverted question mark appear in the selected text field.

Summary:
Go to where you want to post the question mark. Tap 123. Find the question mark icon. Tap and hold ?. Swipe up and over to select . Remove your finger.