The small SMT board is one of my 'stackable' boards that I made a couple of months ago. It has a PIC18F2620 on it (way overkill for this project).
Just below the battery and to the left of the switch is an LED that blinks each time a particle is detected.
The large board is primarily a circuit for generating very high voltages (over 700 volts) at very low currents, necessary for the Geiger tube.
The PIC drives the voltage-booster using PPM (pulse-position modulation, similar to PWM). A small version of the output voltage goes back to a PIC A/D input, so it can actively regulate the output voltage (just like a switching power supply). A pulse from the G-M tube triggers an interrupt on the PIC, and it then blinks the LED. Note that the PIC could easily be used to measure "counts per minute" and such.
When operating, I get one count every few seconds, due to background radiation and cosmic rays and such. I also have an old wristwatch with a radium dial that outputs *many* counts per second when I hold it less than an inch or so from the tube.