Summarize:

You will see the screen dim for a moment to indicate that the screenshot was taken. If the device doesn't have a Windows button, press and hold the Power and Volume Down buttons instead. Your screenshots will be saved to your Pictures library in a folder labeled "Screenshots". You can find your images by using the Pictures app or Explorer in Desktop mode. You can use the Snipping Tool on Windows tablets, but it doesn't work too well with the touch interface.
Press and hold the Windows and Volume Down buttons on the device. Find the screenshots. Use the Snipping Tools if you'd like.