I mean, if you could get your hands on a variable capacitor, you're in business. That was unlikely to be an item you could scrounge up though. The guys in the article managed to find a tube and other parts, so that's quite impressive, but you can still get more minimalist.

The most basic is a length of wire wound around a coil form (toilet paper tube, plastic bottle, etc), the "detector" was a blued steel surface (DE safety razor blade), a safety pin to act as a "cats whisker" (bonus if you can use graphite pencil lead attached to it), some high impedance headphones (WW2 tanker/air crew headsets usually fit the bill), a good ground and as much wire for an aerial/antenna as you could get away with.

Using the length of the coil, and where you connected the antenna, you could kinda-sorta tune for better efficiency at different parts of the band (be it SW or AM). (Longer coil = lower freq)

I made a few of them years ago, and posted the results on my now-defunct blog. The DB is still intact with my files and findings, but my code base is hosed (need to remake it).