Hold in the Side Button, then press and release the Volume Up button. A flash of the screen later, a screenshot is captured. I’ve actually found it easiest to press and release both buttons at the same time, instead of pressing in a sequence. If you forget to release the buttons, you’ll soon see a prompt to turn off the iPhone X.
You can then use the nifty new screenshot tool in iOS 11 to mark it up or share it without having to save it to your camera roll.