Once you have added captions to a video (either generated or uploaded your own), you will automatically see the captions displayed on the video player when you go to the Watch Page.
Captions are displayed at the bottom of your video as white text on a black background. At this time, you are unable to edit the caption text or box. If a viewer moves their cursor onto the video while playing the captions box will move above the player details to ensure visibility (as shown in the GIF above).
Additionally, the captions are set to display by default (default on English) for any video that has captions added. Anyone watching the video from the Watch Page will be able to toggle the captions on or off in the video controls as shown here:
Captions will not be available if you export the video or share/access it anywhere other than the Watch Page.