I'm currently working on a project which is a battery monitoring and reserve system in a car.
I will be using an Uno for prototyping and an Atmega328P for a PCB in the final design.
I plan on using a LM7805 IC on the 12V car battery to stepdown to 5V to power the arduino.
I would like to protect the arduino/circuit from over-current and/or over-voltage on startup of the car (as a car battery can output quite high amps) as well as general use of the car.
What would be the best way of going about this? Fuses, op-amps etc.
First prove with an oszilloscope that you 7805 does not do the job when used propperly. You may want to add an RC lowpass on the incomming side of the 7805 if it proves not to work.
I would add a protection diode to the 7805 input just in case you get a power inversion. They really don't like power connected backward. Besides that, I've found that the 7805 is a pretty rugged design.
And... Current into the Arduino depends on the Arduino, and whatever is connected to it. (Ohm's Law).
A car battery is capable of a few-hundred amps but if you power an Arduino through a voltage regulator, or through the barrel jack using the on-board voltage regulator you'll only "draw" about around 100 milliamps (depending on what else is connected).
I have an Uno in a vehicle powered with 12V through the barrel jack.
There are regulators designed for automotive applications that have better protection than the 7805 (especially if you're using a generic 7805.) The one I usually hear about is the LM2940 (which is pin-compatible with a 7805), but it's pretty old and it might be worth looking for something more recent
I think you need to look up ohms law here. If a car battery is supplying a large amount of current that in no way gets into your Arduino. In fact while the battery is driving the starter motor the voltage from the battery will drop and your Arduino will not be in danger.