On Apple Watch:

Open the Settings app.
Tap Gestures.
Tap Double Tap, then toggle on the switch next to Double Tap on the next screen.
If prompted, tap Turn off Accessibility Features at the bottom of the on-screen alert.
Choose your preferred setting for "Playback" (Play/Pause or Skip) and "Smart Stack" (Advance or Select).

On iPhone:

Open the Watch app.
With the "My Watch" tab selected, tap Gestures.
Tap Double Tap, then toggle on the switch next to Double Tap on the next screen.
If prompted, tap Turn off Accessibility Features in the on-screen alert.
Choose your preferred setting for "Playback" (Play/Pause or Skip) and "Smart Stack" (Advance or Select).

Apple says Double Tap is enabled by the S9 chip's faster Neural Engine, which is why the feature is only available on the Series 9 and later and the Ultra 2. Apple said it developed an algorithm that detects the "unique signature" of tiny wrist movements and changes in blood flow when the index finger and thumb are tapped together.
If you own an earlier Apple Watch model that doesn't support Double Tap, you can always try a similar but more limited accessibility feature called AssistiveTouch, which is available on the Apple Watch Series 4 and newer.