How do they do mirror scenes in movies and hide the camera?

Mr. Smith has a good basic set but missed one of the cooler ones: a set with two duplicate and opposite rooms and the mirror is really just a window (sometimes without even a pane of glass). The actor is in the shot where face is shown, while a double is on the side so you only see the back of their head. I wish I could site movies this has been done in - I know in imdb.com I have seen this method cited at least twice.

Clever camera angles
Shooting several different takes and editing them together.
Software that can remove the cameras.
I'm sure there are other tricks.

Camera angle. The camera is slightly off to one side of the mirror, so that it doesn't film its own reflection in the mirror. The actor then stands directly in front of the mirror so that the reflection of the camera lens (from the actor's point of view) is in the middle of the mirror, but still faces straight forward instead of turning toward the camera reflection in the mirror.

And, it doesn't matter that the actor cannot see his entire body in the mirror, as long as the camera can see it.

If the camera was directly in front of the mirror, the actor would be between the camera and the mirror, right?

You can try this at home, with another person. You play the part of the "camera" and your friend plays the part of the actor.

Its usually green screen.

Usually just the angle. A camera shot at a slight angle will not show.