My niece wants something like this for her engagement party! I have no idea how the tiers are held together - do I need that back part to somehow sit them on? I may just ask her to find something else!
I agree with the others, It is a beautiful cake.
Looks to me like they are fondant or gumpaste pieces cut into shape. The darker ones look like they are a layer of white with a layer of black on top and they dusted. If you look at the inside of the stairs and compare them, they have the same imprint, so the person probably had some sort of mat to use. Or created a template??
One of 2 ways, #1 Use plastic cake dowels, they come in various lengths or buy some pvc piping from your local hardware store. They also come in various widths. Glue with white chocolate the pieces around them to create that box or square look, attaching each piece at its height needed.
#2, Cut foam core to the shape and height, glue on the fondant pieces and attache to the cake or back of the stairs.
I would use the first method.