dgpilot, without an electrical engineering degree, what goes beyond the most simple explanation is probably more than 99% of pilots could understand anyway... if you understand how to use VOR navigation and its limitations/errors, be content with that...
In addition to what airplay has posted, the VOR signal is actaully composed of 4 signals... For your masochistic pleasure, here is the general equation for the VOR signal in space.
Omega = angular frequency of the 30 Hz AM and FM
Omega' = 9960 Hz subcarrier
Omega'' = voice band
Omega''' = 1020 Hz identification signal
= modulation depth (m1-3
k = frequency deviation of the subcarrier (16 ± 1 Hz)
Theta = 30 Hz phase shift equal to the azimuth
Just on note to clarify the post of Airplay, no timing is done in the nav receiver, it just measures the phase difference between the modulated signals. I'm sure there are a hundred sites that people can link to that will show you the phase relationships for the cardinal azimuth locations; It's quite simple actually.
If you want to know how the ground stations are constructed, I can post that for you as well...