How do I detect a switch opening with an Arduino?
Just treat it as a normal push switch.
If there's not already, you'll need to add a pull down resistor, since it's normally closed/ X voltage, but when pushed it is 0 volts, but there will be "static" left in it that your Arduino can't detect. (For a lack of a better explanation; just look up pull up/down resistors if you want to know more.)

WARNING: Nobody else has mentioned this before, so I've taken on the responsibility to do so. Make sure that the switch is operating at less than 5V. (3ish V or above for digital, but you should be able to get away with very little voltage with an analog pin.)

I don't know how isolated the switch is; you'll have to judge how the Arduino will affect the circuit and vice versa. Consider pull up/down resistors like I said. If you don't feel knowledgeable to do this, get advice. It's better to ask advice and wait a day than to not get advice and have no Arduino. (I speak from experience with many gadgets that I tried to rig, yet no Arduinos hurt actually... yet. Haha.)