I'm a little confused on what I need to change - I have a simple 7805 regulator setup with a rectifier before it and a 47u cap after it.
it will run happily and be stable on a 9v battery or a 7.5-12v DC transformer, but I would like to know how I would need to modify this for possible use in a car cigarette lighter.
Can anyone explain what protection I'd need to put in, obviously suitably rated.
You should put 2 100n caps, one in front of the 7805 ad one behind it. The 47µF behind it is not required, its better to put a bigger cap (470 - 1000µF) in front of it.
It should work fine then off a car cigarette lighter - I've made a digital voltage meter with a pic running with a power supply like that in both a honda crx and a civic, never had any problems with it.
You should have smallish capacitors on both input and output, as close to the pins as possible - 0.1uF as Exo suggested is fine - but small electrolytics work as well (1-10uF).
The capacitors are there to stop the device oscillating, and even though it 'may' work OK without them, it's likely to oscillate under some load conditions.