Keeping score is simply a case of incrementing the value of a variable when the player does something that will earn them points. To show the score on screen you can use either a guiText or something like a guilabel:

// using a gui label
var currentScore : int = 0;

function OnGUI () {
    GUI.Label (Rect (10, 10, 100, 20), currentScore);
}

In the case of the guiText you would need to convert the value of the score (which is an integer) to a string, like so:

// convert the variable scoreNumber which is an integer to a string
    currentScore.ToString();

// set this to the text value of your guiText to display it
guiText.text = currentScore;

To increment the value of the currentScore variable, you could use something like the following. This is a modified extract from the Unity Game Development Essentials book where the player collects batteries by walking over them:

static var currentScore : int = 0;

    // A function specifically for detecting collisions with colliders
    // that have had the Is Trigger flag set in the inspector
    function OnTriggerEnter(collisionInfo : Collider){

        // if the current gameObject of the collider stored in the collisionInfo
        // variable has a tag of "battery" (ie, we have hit a battery)
        if(collisionInfo.gameObject.tag == "battery"){

            // Increment the global score variable declared in the by 1
            // ++ is short hand for currentScore = currentScore + 1;

            currentScore++;

            // Play a sound to confirm we have picked up a battery
            audio.PlayOneShot(batteryCollectSound);

            // Remove this particular battery from the scene (the object whose collider we have hit)
            Destroy(collisionInfo.gameObject);
        }
    }

The best way is to notify another GameObject that keeps track of the score i.e. the player or a control GO. Something like this:

function ApplyDamage(damage){
  hp-=damage;
  if(hp<0){
    Control.SendMessage("AddPoints",200);
    Destroy(gameObject);
  }
}

This page explains how to do scoring well. It is about the 4th item down.

To determined if points should be added, add points from the death of the enemy instead of the player. So the player attacks the enemy. The enemy calculates the damage and determines it should die. It calls the Die method.

function Die () {
    MySingleton.Instance.Score += 5;
    Destroy(gameObject);
}