How do film directors film shots where the person is looking into a mirror, but the camera is not shown?

It’s at an angle to the side.

@iamthemob : Even when its a direct shot where the person is looking straight into the mirror?

Yes, shooting the shot at an angle is the simplest way.

Angle of Incidence

They can also use a lot of CGI tricks.

And with computers and a stationary background it is super easy to delete the camera. Take a picture and plop it in as a background replacing where the camera was.

When I was a young kid I could never understand why, if you looked in a mirror in the TV screen, you couldn’t see your own reflection.

Maybe what they’re filming is not a mirror but a transparent glass or even just a frame with everything happening behind without even a glass?

I think I saw the making-of of an advert of a camera that did exactly that. Well, not exactly that. But it seemed like the person filming itself on the mirror, was holding a transparent camera on its reflection. Actually, it was someone else, on the other side of a frame (no wall behind the frame, of course)