How do they shoot the scenes in which a character falls downstair, like in this Revolver clip, for example:
Well, basically, someone pushes someone down the stairs. While the camera is running. Lately, there is special effects to digitally matte a characters face on a stuntman if they want to go an extra mile.
No fake or padded stairs either.
As mentioned above, stuntman and stuntwomen are trained how to fall. In many ways. Falling down stairs is just one of them. Much like wrestlers are trained to take a fall. It gets drilled into them before any thing else. You fall right or you die. You fall and fall until you fall right.