This activator --> NorTempleEntranceHallDoor01 <-- can be found in the Creation Kit.

My question is, how do I set up things in order to use it. What I want is to have the player enter a trigger box which will activate this object and open it.
I tried to do this, but failed. Which script and which properties shall the trigger box use? Should I apply a script to the door as well?

Thanks in advance!

Have you tried the Default2StateActivator script attached to the door and ActivateOnEnter attached to the triggerbox with an ActivateParent from the door to the box? It worked with a portcullis I'm using.