Children using YouTube
Watch with your kid
Simply ask your kids what they're watching and join them. In general, kids are tuning into certain channels or following specific YouTube personalities because they're entertained by them. Many kids naturally want to share the videos they like.
Watch by yourself
If kids don't want to share, get the name of the channel they're watching and watch it later. Watch a few videos by the same creator to get a feel for the content.
If you're concerned about the content your kid is watching on YouTube -- and you've tried talking to them- there are ways of tracking their viewing habits. If they have a YouTube account (which only requires a Gmail address), their YouTube page will display their recently watched videos, recommended videos based on their watch history, and suggestions for channels similar to the ones they’ve watched. Even if your kid deletes her "watch history," the recommendations all will be related to stuff they've watched.