Cut out a section of green screen fabric to match the dimensions of the mirror's reflective surface.
Secure the green screen material to the fabric over the mirror, or in place of the mirror, using double-sided tape.
Light the area the screen is on from an angle that will not be impeded, so that the screen has a consistent color during the scene.
Film the scene with the individuals in front of the mirror.
Film the scene from the position of the mirror, with the exclusion of anybody that will not be having a reflection.
Import the video files into your editing program.
Set each shot up as its own layer, with the main footage as the top layer and the footage from the mirror's perspective as the bottom layer.
Select the green screen in the main video using the eye dropper to remove the green pixels, allowing the reflection footage on the layer below to show through.