How do I make it work and see the times?

Here's how you enable the widget:

1. Swipe down from the top of the screen
2. Tap 'Today' to see your widgets
3. Scroll down and tap Edit
4. Tap on the green plus next to World Time Widget 
5. Click Done in the top right

Swiping down also works from the lock screen.

Here's a video:

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