To capture a moment, tap on the screen while you’re watching something on Netflix to see the various menu options, then tap on the new “Moments” button to pop up a new menu, and then tap the save button. From the Moments menu, you can also see other Moments you’ve saved for that show or movie and share Moments to various apps. You can also copy a link to the Moment to your clipboard.
Netflix gave me early access to the feature, so I used it to make a moment of the best scene in Lost — spoiler warning, obviously — which is perhaps the most Jay Peters thing to do.