To turn on closed captions and subtitles while watching a video on fourth generation Apple TVs: 

 Swipe down on your remote's Touch surface to reveal the Info panel, then swipe right to see the Subtitles panel. Swipe down and select the option that you want to use.

If you want videos to use captions or subtitles for the deaf and hard of hearing by default:

Go to Settings > General > Accessibility.

Select Closed Captions and SDH.

For more information, click here to visit Apple Support.