YouTube uses Flash .FLV video streams. They are broadcasted through the HTTP protocol so you may download them even with your browser (like Internet Explorer, Firefox, Opera).

I suggest you to download videos from youtube using free download manager called Orbit Downloader.

After downloading flash .FLV videos from youtube you may convert them using free audio/video converter called MediaCoder. It can convert to DVD format.

However I don't really suggest to convert do DVD 'coz youtube videos are not of a good quality. They are OK to view in a small windows, not at a full screen on large TV.

To watch youtube videos on your TV you may use a videocard with TVout or standalone devices like Apple TV.

Please note that many new standalone DVD players support MPEG4 format. It might be better to convert youtube .flv videos to it.