Tried the how stuff works site, no joy searching for "VOR" or "navaid" but "VHF omnirange" gave me a link to some data on viral hemoragic fevers
Since I don't have the details handy (I'm in the office and my textbooks are at home) I'll give the short version, which should inspire at least twenty other users to jump in and explain why I'm wrong
VOR and ILS both operate on the principle of phase displacement. When two signals of different frequencies are mixed, the interference between them leaves a "beat frequency" that can be measured. With ILS, the waveform of this beat will vary in shape depending on which of the two signals is stronger. For VOR, there are two signals, one constant and the other that shifts in phase around the station. The two signals are in phase north of the station, and the phase shift (which translates into a beat frequency) equals the bearing from the station, e.g. a 90-degree shift indicates that the receiver is east of the station.
DME is the simplest- it sends out a signal to the station and waits for a reply. Divide the response time by twice the speed of light and you have the distance.