Here's how I would do it...
Figure out how many LEDs you want (based on locations where you want illumination, etc), colors, and brightness, then pick your LEDs. Seems you've done that already.
Each LED with need a series resistor, or you can wire up to a few LEDs in a series with one resistor per "string" or series LEDs. If you have more than a few LEDs, you just need to parallel the strings. You adjust that resistor value to match the LED current (leaving a slight buffer just in case).
As SteveK mentions, use a series diode for reverse protection.
During charging, cars usually get up to 13.5 to 13.8 V, but I calculate to 14V. Using your 3.3Vf, with one LED, you get 14V - 0.7V (typical for a basic rectifier diode) - 3.3V (Vf for one LED) = 10.0V. If the LED says 20mA typical, I would drop that by 10% and use 18mA. R=V/I, so 10.0/0.018 = 556ohms. Closest common is 560ohms. Note that the resistor drops 10V, so power through the resistor is 10 x 0.018 = 0.18W, so you should use a 1/4-Watt resistor here.
Is you use 2 resistors in this string, then you get 14 - 0.7 - 3.3 - 3.3 = 6.7V (dropped by the resistor), so R = 372ohms, or I'd just use a 390ohm resistor here, and power works out to 0.12W, so you can get away with a 1/8W resistor.
The voltage can drop to about 12V in certain conditions, or down to 10V or less during cranking (but are you really worried about your LED brightness at that point?). With the resistors calculated above, do the math again for 12V and see what the current is, and you'll see how much brightness variation there will be. The more voltage the resistor drops (compared to the LEDs), the greater the current variation (and hence brightness variation) as the car's voltage varies. But you get to use less resistors this way.
Yes, you can use a regulator to regulate the voltage, or better, use a current regulator. I don't bother unless I'm doing a lot of LEDs, and want to not waste so much power in heat. If I do, I'd use a LM317 current regulator, and the datasheet shows how to calculate the values of that.
BTW, yes I know there's an absolute maximum current for the LED which will be above the typical current, but that's in perfect conditions, and a car can get quite hot.
Cheers,
-Neil.