When I am trying something new and challenging for the first time, I like to take the pressure off of myself by making a crude prototype from secondary wood I have on hand with the explicit intention of throwing it away. I have a large stack of alder which is perfect because it works easily.
You can watch the program, but I want to mention a couple of issues I ran into. After layout, the first thing Roy does is make internal vertical cuts along the sides of the "hinge leaves," which, predictably, he has vintage gizmos for. You drill a small hole in the corners and then use a hack saw blade on which a sharp point has been created and a handle attached to start from this hole and open up the cut. I was able to make the blade by using a pair of tin snips, but I don't have the vintage handle, so I just used the blade. Took a very very long time, perhaps because it was a fine blade and I couldn't exert much downward force. Roy then switched to a small keyhole saw to complete the cut. The keyhole saws I can find around here have very thick blades which would detract a lot from the appearance of the stand. I hit on the idea of using a jig saw blade, which seems to work and is thinner. I am going to make a handle for this jigsaw blade before my next attempt.
Next comes chiseling out the hinge. That went smoothly until I got to the nearly vertical part of the hinge. My bench chisels are too thick to use. Roy uses a very thin paring chisel, which I don't have, so I just cut away the hinge enough to let my bench chisel fit (this is just a prototype). I think a carving chisel might work better than a paring chisel and I am going to look for one. If I understood him correctly, he made these in the past with a bevel rather than rounding the hinge, so this is another alternative. I think it might look better and you might be able to round it over after the stand is opened. Roy points out that you can use a shoulder plane to clean it up once it's opened and this would make things a lot easier. You just have to avoid spelching by putting a slight bevel on the sides of the leaves before you use the shoulder plane.
Anyway, here is the result. I am quite pleased actually, as it accomplished its intended purpose. It's very crude but I learned what I need to know to improve. I think these would look especially nice if you chose a board with a prominent grain pattern that would accentuate the fact that the stand is made from one piece of wood.. Now it's into the burn pile!
Give it a try. I found it a lot of fun.
Update: A friend made me aware of a short video by Chris Schwarz on the Popular Woodworking site that addresses both of the issues I ran into. Coincidentally, I had reached the conclusion that the methods he demonstrates are the way to go. Here it is.