This depends partially on the make/model of the car, but there are several different ways depending on what your goal is.
With some newer cars, it's possible to feed data to the computer - although I really would not do that.
The best way is going to be adding a relay to one of your circuits and having the Arduino control the relay.
There are several questions you're going to have to ask yourself though:
- Do you want it to only cut ignition (key in ACC? Or also all accessory circuits (i.e. key in OFF position)?
- Do you want it instantly off?
- Do you want your Arduino to also interrupt with the startup sequence?
I'm sure there are more considerations as well, but those are just a few.
I think the simplest way would be to put a normally closed relay on the ignition line and wire it to the Arduino as the control. This way when the Arduino says to, you can cut ignition for a set amount of time (1000 ms) then when the car is off, or the Arduino is not sending a "kill signal" then the relay will be closed and allow for normal operation.
Apply caution when you start messing with core electrical functions like this. If you wire things wrong, or start messing around with the cars ECU or PCM you run the risk of damaging expensive and sensitive components.
I assume since you're playing around with the Arduino in this way you're at least somewhat savvy with electronics, but you do want to be careful. Depending on the car, some computerized components can get very expensive very fast.
Additionally, there are some parts of the automotive electronics/ignition systems that can be hazardous to your bodily health too - so always be careful!