I was given a DVD of the movie "Theramin" - while not terribly technical the history of the device is quite interesting. Robert Moog of Moog synthesizer fame had quite the interest in theramins and published an article in th 50's - complete with schematic. I googled on "theramin schematic" and found it.
It appears that one significant challenge with the original design is the radiation of RF - a theramin is simply two radio frequency oscillators on very nearly the same frequency - the difference being the audible note. The radio frequency of one oscillator is changed by the promity of the hand or other significant object.