
In this video, I demonstrate cutting a 1x8" board to size, pre-drilling three pocket holes and three regular holes, then screwing it into the treads. This should work for any staircase with wood treads and a little bit of a 'nose' or overhang on each tread.
Mentioned in the video - Kreg Jig K4 Pocket Hole System: (though you can fasten the boards another way if you don't want to use pocket holes!).