You may have Apple TV to cast directly from their iPad or iPhone to the Apple TV and have it shown on the TV screen.
It should be noted that this is not a television set; rather, it is a streaming unit that plugs into the TV and operates with Wi-Fi or Ethernet.
Open the YouTube app. Select the video you want to watch and tap the Cast icon. You have to give YouTube permission to connect to streaming devices on your local network to cast to your TV. Select the device you want to cast to and wait to connect.
do they have cable? many cable boxes now have youtube and netflix built right in.
easiest option though is something like a roku or apple tv streams directly and won't need to "cast" from another device. they plug into the tv and use wifi to access many different streaming services including youtube