Step 6: An Explanation
To explain how the circuit works, by my understanding, it goes like this: When the circuit is powered on (after you reset it to be in an off state) the coil acts like an antenna waiting for minute electromagnetic frequencies to come in contact with. While it waits, the transistors are less biased to pass current and are in an off state as well, much like a switch. Since these transistors are off, they don't pass large enough current to trigger the Schmitt Trigger and the lights and sirens remain off. Once there is a large enough disturbance in the EM field (such as a person entering or leaving it), the field that the coil thought was stable becomes unbalanced and more signals are received (because of the human presence receiving the signals and throwing them all over the place) thus more current is produced in the transistors which gain enough oomph to trigger the Schmitt Trigger and sound the alarm. The transistors are recognized in two pairs called Darlington Pairs which use the previous transistors emitted current to attempt to drive itself. With them in a 4x series the current gains through each of the four stages which allows the very, very tiny signals from the coil to be amplified to the point where they can drive the Trigger. In less exciting news, the switch you installed simply counteracts the on cycle by passing current to the reset pin, thus resetting the chip to an off state. You're probably wondering why the EM field created by the circuit itself isn't triggering the alarm. Well, that's a good question, but not unanswerable. The field around these are strong enough to trigger it but since these fields are stable, the coil doesn't really care about them and won't trigger. If you'd like to test this, take the coil and place it near a track that you can roll a metal marble down. Does it trigger? Touch the coil with your hand and touch a radio antenna. Does is trigger?
I hope you had fun building this and I hope you find it useful to you. With a microcontroller and a few modifications you can turn this into a power saving light control (walk in your room and it turns the lights on, stay still for too long and it shuts itself off) or use it to detect those pesky raccoons that always raid your garbage at night. Whatever you do with this, have fun doing it!