To enable closed captions:

Apple TV 3rd generation or earlier
  1. Hold down the Select button on your remote for three seconds to reveal the Subtitles tab. 
  2. Select the option that you want to use. 
Apple TV 4th generation & 4K
  1. Swipe down on your remote's Touch surface to reveal the Info panel.
  2. Swipe right to see the Subtitles panel. 
  3. Swipe down and select the option that you want to use.
You can also turn on closed captions directly from the CBS All Access Live TV player by selecting the "CC" button on the video screen.

If you'd like to turn on closed captions by default:
  1. Go to Settings > General > Accessibility.
  2. Select Closed Captions and SDH.