In the 1920s the U.S. Government actually distributed literature on making crystal radios. Soon crystal radio sets will no longer work. In February of next year analog TV will cease in favor of HD TV. It is expected by most parties that despite severe problems, radio will go the same way, both AM and FM if you side with Clearchannel's Jeff Littlejohn. Whenever that happens, if it happens, these simplest of tuners will die.
A crystal radio requires no direct power source. It is entirely powered by the radio waves it receives. This is the simplest kind of radio receiver. It's very difficult to name a single or most important inventor. But that didn't stop me from writing about many of them in the past. [Before you nit-pick I'll state for the record that this is the simplest of all radios.] I'll list the parts below but only one of them really needs additional explaining, the diode. I'll get into that in steps, but first lets' cover the radios components:
*I've covered this here.
Loops of wire, usually copper. Tuning different frequencies is manages with fewer or additional turns of wire in the coil. Iit needs to be grounded. Coil + capacitor = resonant circuit.
This is where the crystal comes in. It's not a lump of quartz. The octahedral crystal is a lump of galena a.k.a. lead sulfide, an ionic compound of lead and sulfur. A wire contact is used to form a junction with the crystal until it forms a diode. The wire is called a "cat's whisker." I hate the name but that's the nomenclature. The wire is usually phosphor bronze. To tune, one literally had to probe the surface of the crystal until it generated sound confirming the complete circuit.
Note: There are also iron pyrite and silicon diodes but they are less sensitive. Modern crystal fans use germanium. The Schottky diode is a silicon diode. Walter Schottky's design was sound, and compensated for it's lack of sensitivity with greater efficiency. But suffered from thermal instability. In other words, it gets hot enough to break shit. See below.
More complicated was connecting the diode to both the coil and the earpiece. The normal heat of a soldering iron could damage the already irascible wad of galena. This was often instead soldered with wood's metal. Wood's metal is an alloy of bismuth, lead, tin, and cadmium. It has a melting point of under 160 °F. Still, it releases toxic fumes at that temp. This was really truly such a pain in the ass many people just improvised clamps.
You need to ground the circuit, this is usually between the antenna and coil.
For a crystal set, these need to have high impedance.
The basic way it functions is that the antenna receives the signal. The coil stores the energy in it's magnetic field. Through it the wave energy moves to the diode. The diode rejects half of the alternating current converting it to pulsating DC current. This allows the headphone to work. If you fed AC current into an earpiece the alternating sides of the wave cancel each other out and you get an amplitude of zero. More here and here.