Thx for the feedback! About the 3rd resistor: read somewhere that this could help block any not wanted V gettin into the arduino but I wasn't sure about it either. I will skip that then. So if got the curcuit... just have to build that then.
Is the picture right then?
Is there anything else I have to be aware of when I build this? Cause I tried to build a (ok some mistakes in it; was more like V2) similar thing earlier and now my old arduino doesn't work anymore... don't want to deal with that again.
PS Don't know how this software work 100% so the resistors are wrong and the LEDs may be pointing the wrong way too

ignore that^^
PPS So fungus: "only the grounds are connected", so I should only connect the 3 cables in the "black" line (from the picture, meaning arduino gnd, transistor emitter, 12V -)? Or do you mean something else?