Like the iPhone and iPad, your Apple Watch has the ability to take a screenshot and save it to your Photos. Select the screen you want to take a picture of and press the Digital Crown and Side Button down simultaneously. The Apple Watch will make the ever-familiar shutter sound effect and the resulting screenshot will be saved on your iPhone Photos application.
An example of Apple Watch screenshots viewed in Photos:
A captured Apple Watch Home Screen:
An Apple Watch screenshot downloaded to the Mac. On a 42mm watch the result is a 312×390 PNG: