how do they film scenes in films where the camera is directly looking into a mirror?

There are a few methods that this is achieved.

Something that's most likely not beneficial to you is how they film this one. They have a set, and there's a hole in the set. They have the walls that are facing the camera all prettied up, and the ones that aren't usually are pretty dull.

This next method is more common (I'd assume). The camera is at an angle so that the camera isn't visible in the shot.

Of course this isn't practical in your senario, but I thought I'd throw it in. With animation, the camera isn't a physical object, so you don't need to worry about it being in the shot ;)

i have no clue really. but if i were to use it i would use maybe a green screen with like black dots on a couple places on it and the green screen all around the camera. then motion track the dots to cover up the view of the camera then do green screen magic. I'm not a film person and have never don't anything like that so i have zero credibility ha. I've just always wondered the same thing and thats all I've been able to come up with. if i were you id just shoot at an angle though seems easiest.