The basic circuit
The trapdoor is armed and disarmed using this littleBits circuit. Just turn the dimmer switch until the bar graph lights up, and it's ready! Once the cloudBit receives an input signal, it will output that signal in Minecraft.
The trap door mechanism
Here are the inner workings of the trapdoor itself. A set of pistons work in tandem to open up a 2x2 area in the floor to a deep pit. A single redstone signal toggles the trapdoor between open and closed.
The AND gate
This logic gate controls whether the trapdoor mechanism receives a redstone signal, which outputs from the bottom. The left side receives a signal from the chest whenever it opens. The right side contains the bitCraft piece, which receives a signal from the cloudBit and outputs a redstone signal when the dimmer is turned on. The gate will output a signal only when it's receiving a signal from both the left and right sides.
The alert enhancement
Simply add an LED or a similar littleBit onto the output end of the cloudBit. This will become our alert whenever our trap has snared a victim.
The collection zone
At the bottom of your pit, you can arrange hoppers to collect the items of your victim and deposit them into a chest. If you run a comparator off the chest followed by a repeater, it will output a strong redstone signal whenever the chest contains items. Just run that signal into a bitCraft block and it will pipe it right back to your cloudBit for output!
The final product
Here we see the trap is armed (green light from the bar graph), plus someone has fallen into it (white light from the bright LED!)