I'm writing from a Skyrim perspective just so you know...
I assume that by "parent script" you are referring to the script that your script extends or to put it another way, the script associated with the object type of the object holding your script.
Other than a few top level scripts, every script extends the capabilities from another higher level script or parent if you will.
Actor extends ObjectReference because all actors are ObjectReferences
ObjectReference extends Form because all ObjectReferences are forms
Form does not extend anything because it is a top level script
A script assigned directly to an actor can use any functions and events from the Actor, ObjectReference and Form scripts
The type of script to extend is determined by the object holding the script. If your script is on a quest, it will extend Quest. If the script is on a quest alias, it will extend ReferenceAlias.
When you create a script from scratch in the CK there should be an Extends option. Here you would select the script associated with the object type that will be holding your script. I noticed on FO4's Hello World tutorial that it does not mention the Extends information. Neither does the Skyrim version but it does contain an image showing the field.
Please link the tutorial that you are using, I couldn't find a basic quest tutorial on the FO4 side of the CK wiki. At least not one that went to an empty page.