First off, script calls are used with the 'Script' event command, located at the very bottom right on tab 3. 'Comment' will do nothing for you (however, some scripts say to use Comments in order for their scripts to work, so be sure to watch for that).
Starting the counter should be done in your quest-giver event. The 'id' can be any integer number, so long as you remember this number to refer back to later on. If you accidentally use the same number for a second counter, you're going to override your first counter and lose your count. 'enemy_id' is an integer associated with the enemy's database ID.
This will start counters for how many Ghosts and Zombies you kill.
$game_player.start_counter(1, 1)
$game_player.start_counter(2, 9)
Now go and be happy killing all the monsters you want.
When you return to your quest-giver event, use a 'Conditional Branch', go to the 4th tab and select the 'Script' radio button. In the text box, paste this:
$game_player.get_counter(2) >= 5
If your player kills 5 Zombies or more, this conditional branch will return TRUE and should reward the player. Here's an example:

The
stop_counter script call is best left for situations such as "Kill 10 Ghosts in 1 minute!", where you start the counter for number of Ghosts killed and starting a timer with the event command 'Control Timer'. When the timer hits zero, you can then call
stop_counter.
I don't see much of a use for
total_killed unless you NEVER use
stop_counter once in your game.