I've update the post with a new image. The LEGO plate thickness = the space between the studs. All you need to do is wedge the plate between the studs and it will hold it perpendicular to the gray base plate. You can also use a normal brick to connect the gray base plate and hold the back of the legs of your minifigures.
Have fun making the display.
I'm looking at making this as a birthday present for my friend. I can't quite see (or understand) what you've used to make the figurines stand up? Can you please help?