I've written about foxhole radio before. But back them MAKE hadn't made a nifty video on how to make one yet. The instructions are simple, and even cover some basic problems that may come up in the process. The Tools and materials are very simple. If you are even reading this post, you will be able to do this.
You'll note he had a little trouble with the razor blade. The rectifier is a little unclear for me still though. The pencil lead is a mix of clay and graphite. Knowing that the clay isn't a part of it we're making a connection between graphite and steel. So in that model the razor blade is the whisker and the pencil is the crystal. It's sort of backwards to the traditional idea of a crystal detector.
Graphite electrodes were used in Tungar rectifiers, and mercury arc rectifiers in early car batteries. This was a diode of sorts, used to convert AC to DC. This was around the early 1920s. More recently graphite has been used in Schottky Diodes. More here.But I'm not sure why the razor has to be blue. You can steel blue by heating it (to 530 - 600 F) as in the video but what does that do to the steel? I have also read that you can blue steel with a solution of sodium thiosulphate and lead acetate. There is no way to know what method was used on that specific razor blade. But any non-conductive coating could act as a dielectric. My thinking is that the heating here actually just burns off a lubricant (or other coating) that interferes with the connection.