This display system uses a technique that is often referred to as Pepper's Ghost. It was first invented by Giambattista della Porta in 1584 and has been commonly used in theatre. Some of its famous uses include Alexander McQueen's performance with Kate Moss, Tupac's CG concert cameo, and numerous Hatsune Miku concert performances. Although "hologram" is often found in the title of these display systems - they have no holographic qualities. A hologram refers to a specific medium that stores image data through a laser, a holographic substrait and interference pattern. Pepper's Ghost uses a much simpler technique that merely reflects an image off of a surface to create an illusion of a 3D object floating in physical space.
Step 1: Materials
In order to create a Pepper's Ghost effect, there are two types of materials commonly used. The first is a transparent material that has a reflective surface. Glass would work for this, but a cheaper, lighter, and easier to use material is acrylic plexiglass. When using a transparent acrylic sheet, take a look a both sides as one side is always more reflective. The more reflective side should be facing the image source. Another material that can be used is a scrim or semi-transparent piece of cloth (most commonly being black). Although a scrim won't reflect the image off of it, it can indeed catch an image as a movie screen might. A mirror or semi-transparent mirror would also work in order to reflect an image off of it, but you would lose the illusion that the object is floating mid-air.