This is not a simple process and there's many possible things that might have to be done. Any process is going to require a learning curve.
Try using iDVD if you have it. If you don't then authoring a DVD is pretty involved. Do you have toast? Check Burn.http://burn-osx.sourceforge.net/Pages/English/home.html
Also realize that Youtube video quality is likely to look terrible on a TV.
Check the licensing on the video. Many YouTube videos are copyright and we're not allowed to assist in copyright violation on this forum.