The Activity app on Apple Watch runs automatically in the background, estimating results including all active and total calories burned, including during general daily wear and any workouts.
Active calories are reported via the Move ring in the Activity app (they include active calories burned during general daily wear and during any workouts) and can also be viewed via the companion Activity and Health apps on the paired iPhone.
Total calories (active calories + resting calories = total calories) can be viewed via the Activity app on your iPhone:
On your iPhone, in the Activity app, go to: History (tab) > select a day > scroll down to the Move chart > swipe left on the chart to view Total calories.
Active and Resting calories can also be viewed via the Health app on your iPhone:
On your iPhone, in the Health app, go to: Health Data (tab) > Activity > Active / Resting Energy.
More information: