Using Car Charger (12V Output) to power RGB LED strips and Arduino

Hello,

I am fairly new to Arduino and electrics, so please excuse my incompetence. And I have tried looking for this specific setup on several forums, but none was found.
First of all: I am not powering anything from my car's battery. In my car, I have a charger outlet (cigarette type) which outputs 12V. Can I use this to power an LED Strip?

If I can, which kind of adapter would I need?
Basically, I want to do this: http://learn.adafruit.com/system/assets/assets/000/002/692/medium800/ledstripfet.gif?1353964350

But I only have an Arduino UNO, which doesn't have a 9V output pin. So I want to use my 12V output charger in my car instead.

The main thing I am stuck on is how to connect the strips to the Arduino with all the transistors with an external power supply? And, how do I connect the ground for the Arduino to the ground for the LED Strip?

Edit: I just found this, Female DC Power adapter - 2.1mm jack to screw terminal block : ID 368 : $2.00 : Adafruit Industries, Unique & fun DIY electronics and kits
Can I maybe use this to get a positive and ground wire from my car's 12V output?

You need to understand that current is important... so yes 12v rating is good but if it's only 200ma it's not goimg to work...

Also 9v out on an arduino ? That's new?

Oh yes, thank you I haven't forgotten about current. I bought a 12V 2A adapter, I think that would work for 2-3 meters of Led strips?

I am using ESEEKGO LED car charger. It really work well. You can have a try. https://www.amazon.com/Charger-ESEEKGO-Adapter-6-6ft-Samsung/dp/B01NA8TWX9/ref=sr_1_49?m=A2PQ5VQHSRWEC5&s=merchant-items&ie=UTF8&qid=1480559480&sr=1-49&refinements=p_4%3AESeekGo