I'm a mechanical engineering major for a reason. This is all voodoo magic as far as I'm concerned.
I believe that input voltage on the green wire (at the transistor base) ought to complete the circuit for the relay to close - but uhh it maybe doesn't? I don't even know. I do know that if I touch the end of the green wire to the part marked "Yes" on the photo the relay closes. Touch the other side of the diode? Nada.
The red line is +5V, the black is GND.