Well, the first thing is always have to ask the YouTube owner channel for permission to see if they're gonna allow you and your visitors to add subtitles in their videos. If they decline, ask them if they would be willing to allow crowd-sourced captioning. This setting lets users edit YouTube’s automatically generated transcript to create captions for free. Note, however, that this means you need to personally edit (or check the quality of) those captions for adequate accuracy. If the owners do not want you or your visitors adding the subtitles or doing anything their videos then don't do that. It is legal to transcribe and add captions to YouTube videos that don’t belong to you and it is under circumstances of fair use.