It's easy to watch high definition YouTube, Vimeo and Netflix videos on a digital TV using a newer notebook PC or MacBook and an HDMI cable. Insert the HDMI cable into the socket on a PC notebook. The other end connects to your TV. I use the cable from my DVD player. If your computer doesn't have an HDMI socket, try VGA or DVI and audio cables instead.
The default resolution some YouTube videos might be a lower res 360p. Click on that number and see if there is a higher resolution available (720p or 1080p). Click the full screen icon (to the right of the resolution icon) to fill your TV screen with HD video (Esc exits full screen view). Keep in mind that you need a fast Internet connection for HD video, otherwise there will be many delays as the video "buffers". If there is no audio, check the mute button, or you may have to go into the Windows control panel or MacBook system preferences and select TV or HDMI as the audio destination. Remember to switch the audio back to the computer when finished watching on your TV.
Here's an HD video of the Billy Jones Wildcat Railroad in Los Gatos, California.