If you have an Apple TV and you have an iPhone or iPad:
Look for this icon 
on the bottom right of the video you want to play (while using the Safari web browser). On an iPhone you will have to hold the phone horizontally for the icon to appear. Tap it and select your Apple TV. All videos will now play on the Apple TV until you find that icon again (on any video) and turn it off.
If you have an Apple TV and a Mac running the operating systems El Capitan, Sierra or High Sierra:
• You can follow the same instructions as above for the iPhone or iPad.
• Please do not use “display mirroring” where everything on your screen is also played on the TV. Even when watched in full screen, the videos will be choppy.
If you have an Apple TV and a Mac running an older operating system, or a PC desktop or tablet:
• This requires installing extra software that I won’t describe here. If you also have an iPhone or iPad it would be easiest to use it for watching on your Apple TV.
• (on an older mac OS) Please do not use “display mirroring” where everything on your screen is also played on the TV (not just the videos). Even when watched in full screen, the videos will be choppy.
If you have a Chromecast and a Mac or PC (laptop or desktop):
• Just download and use the newest free version of the Google Chrome web browser to surf this website.
• Look for this icon 
on the top right of the browser window. Click it and select “Cast” from the menu. Now all videos will play on the Chromecast.
If you have a Chromecast and a phone or tablet:
• On an iPhone or iPad this requires installing extra software that I won’t describe here.
• On an Android phone or tablet, this article explains one way of doing it using Firefox. I don’t own an Android device, so I haven’t tested it.