Character Controller question...

Questions & Answers
1

How can I invoke a function the moment that a character controller touches a ground?

2

Dont know if you’re wanting it to do it when you hit a specific surface, or EVERY time it lands on something…

Attaches to the character controller

This will work EVERY time upon landing after leaving the ground → 

var controller : CharacterController ;
var wasAirborne : boolean = false ;

function Start(){
   controller = GetComponent(CharacterController) ;
}

function Update () {
   GroundCheck() ;
}

function GroundCheck(){
   if(wasAirborne){
      if (controller.isGrounded){
         //!!--This is where your code for calling or doing your
         //other stuff after landing would go
         //e.g. DoMyLandingFunction();

         Debug.Log("We touched down!") ;
         wasAirborne = false ;
      }
   }
   else{
      if(!controller.isGrounded){
         wasAirborne = true ;
         Debug.Log("We're airborne!") ;
      }
      else{
         wasAirborne = false ;
         Debug.Log("Just walkin around now...") ;
      }
   }
}

//function DoMyLandingFunction(){ here }
Otherwise, if you're wanting to call/invoke something upon contact with a specific object you could use OnControllerColliderHit or modify the code above to suit your need.