
Frank T. answered 03/27/19
Ph.D. in Film & TV Studies (UCLA) with 35 years of Teaching/Publishing
In most cases, it's fairly simple. They just angle the shot so that the camera is not facing the mirror head on; it's at a slight angle.
There was a MAJOR error in an important film that involved a mirror shot. The movie was The Turning Point (Herbert Ross, 1977), which was nominated for the Best Picture Oscar that year. Set in the world of ballet, there's a scene where the dancers are practicing at the barre with a wall-length mirror behind them. When I saw the film at its premiere, you could clearly see the entire crew, director Herb Ross, and the camera in the mirror! Whoops!
Shortly thereafter, they must have reshot the scene -- or just cut it entirely -- because that shot was gone.