Contrary to what some people may think Fur Elise is a good piece to know. Once learned it's not too difficult, it sounds nice in competent hands and everyone recognises it and most people like it. I've used it several times for company and even in recitals, it's always well accepted. So it's worth learning, IMO.
As to teaching ones self how to play Fur Elise via You Tube, I'm in the camp with the responder that said basically that's just one piece of music. Now would the OP be intending to learn every piece of music in this fashion ? As the difficulty level goes up this will get near impossible. Learn To Read, because I assume that Fur elise is not the end of the line in the learning curve !