Your car's voltage may be "worse" than mine, but I'm running an Arduino in a car with the car's "12V" into the Arduino's Vin pin.
The Arduino's on-board regulator is a reasonably-good "filter". The Arduino specs say:
The board can operate on an external supply from 6 to 20 volts. If supplied with less than 7V, however, the 5V pin may supply less than five volts and the board may become unstable. If using more than 12V, the voltage regulator may overheat and damage the board. The recommended range is 7 to 12 volts.
The biggest concern is usually if you are powering lots of "stuff" through Arduino's regulator. The higher the applied voltage (and it can be about 15V) the more current you are "dropping" across the regulator and the hotter the regulator gets. Also, the more current you put-through the regulator the hotter it gets.
So for example, if you are just running the Arduino and a couple of LEDs you should be OK with the vehicle-power.
First, how a zener actually works and how it is wired up,
A zener alone won't do it.
An LM7812 voltage regulator is easy to wire-up (just add 2 capacitors) and the TO220-package version can dissipate more power than the Arduino's "little" regulator. Or, if you're running lots of 5V stuff and you need more 5V current, you can buy a 5V switching regulator board/module and power the Arduino off that (bypassing the Arduino's linear voltage regulator).
P.S.You
do need to protect the Arduino's
signal inputs from anything greater than +5V (or anything negative). A simple zener & resistor or regular diode & resistor circuit can do that.
Here's a link, if you are connecting anything from the existing car electronics to your Arduino.