I might be mistaken, but I think Rik wasn't quite clear on your original question (neither was I, until you clarified it in your second post). His shooting technique would get you a great shot for someone talking to an inanimate mirror. But if I understand correctly, you want to be able to speak to a magical mirror, one that will talk back, like a real conversation?
If that's the case, then Nate's method a great way to go. However, it does depend on which software you're using (they don't all handle keying the same).
Another way to do it (if you've got the right software) would be to rotoscope the edges of the mirror. If the camera is locked down, and if the shoulder doesn't ever cross the line that would be rotoscoped, this would be the easiest and fastest rotoscoping, ever.
If you don't have software that can easily key (green screen) or rotoscope, you can always use an old-school split-screen effect. 80's sitcoms used this effect all the time, when the lead would meet their long-lost forgotten twin/doppleganger. I used it in my very first short, with a shitty computer, and a really old version of Premiere, and it worked brilliantly. All you gotta do is lock down the camera, keep the lighting perfectly consistent, and don't allow either image to cross over the other. And then in post, you just crop.
Your easiest solution depends on your software's capabilities. Let me know what you're working with, and I might be able to give you a little more detail on how to make this work.