I was wondering if it is possible to add a pickup to a classical guitar (essentially making it an electro-acoustic) and how this would be done? I have seen nylon-stringed guitars with pickup most notably the Yamaha Silent Guitar.
a piezo pickup, just like in other acoustic guitar pickups
You would need a piezo or one of the vibration ones you put on the body that pic up the sound that way, mounting a standard pickup to it won't work with the nylon strings.
piezos or transducers are used for classical guitars and banjos etc