Hook Siri into the audio system, hook the screen into the auto video system. Apple has provisions for this. The auto makers need to put it into their cars. For example the Siri button should be on the steering wheel. Eyes Free implementations put it on the hang up button for the car phone, for example. Tap it while not on the phone and you get Siri. They also need a way to switch their display from its normal functions to showing the phone video output. A button on the console, perhaps
On Apple's side, two main things are needed. Siri must do much more. This includes controlling third party apps. To do this they must open a Siri API. In a car, I want to verbally say zoom the map in and out, an API will allow this stuff.
Apple must also be able to show more on external video, such as a car display. Mirroring isn't enough. to show its maps on the car display, it needs to send a nice 4:3 image at car display resolution, not a tall thin or short wide mirror of the phone display.