‘Because they hoodwinked a very powerful magical object!’ said Moody. ‘It would have needed an exceptionally strong Confundus Charm to bamboozle that Goblet into forgetting that only three schools compete in the Tournament ... I’m guessing they submitted Potter’s name under a fourth school, to make sure he was the only one in his category ...’ [Barty Crouch Jr/Mad-Eye Moody]
Goblet of Fire - page 245 - Bloomsbury - chapter 17, The Four Champions
Thought about this when I was paging through Goblet of Fire recently and I kept coming back to one part. I see that CJM listed the passage in his answer that I'm going to quote; however, I'm putting it down again because I have a different take on that paragraph.
We already know Harry's name was added to the goblet by a second party; this is evident at the beginning of the book when Harry's name pops out of the cup to begin with.
I interpret Goblet of Fire canon to mean the primary element in Harry circumventing the powers of the Goblet of Fire is by someone first bewitched the goblet to forget it was to pick only three champions from three corresponding schools (which raises the issue of whether the goblet is sentient like the Sorting Hat is?). Forgetting is something a mind, a brain, does. The champions were not picked like a raffle; the Goblet of Fire chose champions based on, we might assume, merit, ability, intelligence, etc. So in some way it must think.
It is the act of forgetting that allows the Goblet of Fire to consider a fake entry as if it were legitimate, because it no longer knows the number of champions chosen should be limited to three.
Yes, Barty Crouch Jr put Harry Potter's name into the cup under a fourth school's name and that allowed Harry to be picked. However, if the goblet had never been forced to forget its own guidelines, it would have ignored that piece of paper with Harry's name and the fake school on it.
So, Sachin Shekkar's question is actually: The Goblet of Fire was designed to choose 3 participants from that list, one from each school? How exactly was the "3 contestants, 1 per school" limitation overcome? It was overcome because the goblet forgot it was supposed to limit itself. And this was achieved by Crouch Jr placing a very powerful Confundus Charm¹ on the goblet.
The Goblet of Fire had to be made to forget. It had to be made to forget it could choose only three champions from three schools. Placing Harry's name into the goblet is secondary to this -- it cannot happen unless the goblet first forgets its purpose and guidelines.
Yes, the goblet forgot how it works. Second to this -- and only second to this -- Crouch Jr was able to slip a piece of paper into the Goblet of Fire with Harry's name and the name of a fake school on it. Not remembering it could only choose three, the Goblet of Fire spat out Harry's name as the fourth Triwizard contestant.
¹I'm kind of scratching my head at the idea a Confundus Charm would cause the Goblet of Fire to forget. That particular power seems more consistent with a memory charm, or Obliviate. The Lexicon lists under Confundus Charm: "confundo" L. to mix up, jumble together, confuse, bewilder, perplex. Obliviate shows: "oblivisci" L. forget.