Transducers for sensing brain waves which can be made at home?
It's not an EEG, but my experience building an EKG circuit from scratch might help you a bit. (Not sure if EEG is easier or harder). A few old OP27's configured as an instrumentation amp (wikipedia) on a breadboard provided sufficient gain to get from sensors to an output comparator, which drove an LED. The power source was a 9V battery, both for safety and reduction of 60Hz noise input. The sensors were nothing more complicated than leads soldered onto two shiny new pennies. For contact gel, a mixture of alcohol hand-sanitizer with a little baking soda did the trick. Just the two sensors feeding the differential input of the instrumentation amp (and the usual fiddling with resistor values) was all it took to make the LED blink in sync with my actual heartbeat.  It was a quick, cheap, satisfying hack.

For an EEG, you obviously want a more analog output than just the on/off from a comparator, so you'd want to run the amplifier output into an ADC. I'd say try running the signal into a PC sound-card input, but not sure that PC sound inputs have much response in the frequency range you want, which is probably in the 1Hz to 40Hz range. You'd probably also want more than a single pair of sensors. If you stick with a 9V battery for power, you will have a very hard time electrocuting yourself, and won't be able to drive any signals into your neural nets. 

btw, if you're really worried about signals going into your brain, the only thing that does that AFAIK is "transcranial magnetic stimulation". You won't build that by accident.