How does a video clip get from TV/DVD to youtube?

So I was watching The Muppets Take Manhatten on tv and missed the song “Saying Goodbye” so I went to youtube to look for it but it’s not there. It got me thinking of how a clip gets onto youtube.

I’m pretty sure if I owned the DVD I could just pop it in my computer and there’s a software program out there that can convert it to a format compatible to upload onto youtube….Do I have that right? If so, is that the only way?