A boy climbs, and is pushed
Bran Stark sees what he should not have seen in a tower at Winterfell and is thrown from the window for it. He lives, which surprises everyone, and the attempt to finish the job puts a Valyrian dagger in Catelyn Stark's hands and sets the Starks and Lannisters at each other's throats.
The fuller tale
Bran Stark climbed everything at Winterfell and had done since he could walk, and his mother had asked him a hundred times to stop. On the day the royal party arrived he climbed the broken tower, and through a window he saw the queen with her brother, and the brother crossed the room and put him out of it.
He lived, which surprised the maester and everyone else, and he did not wake for weeks, and when he did he could not remember why he had fallen and could not use his legs. Then somebody came in the night with a Valyriansteel dagger to finish him, and was stopped by a boy's mother with her bare hands on the blade and a direwolf at the door.
That dagger is what starts the war. Catelyn Stark took it south, was told by a friend of her family that it belonged to Tyrion Lannister, and believed him ÔÇö and one of the two facts in that sentence was a lie planted by the man telling it.
The lie that lit it
The whole of the War of the Five Kings can be traced back to a single sentence spoken by Petyr Baelish in a room with no witnesses. Catelyn seized Tyrion on the strength of it; Tywin raided the riverlands in answer; Ned was hurt in the street over it; the North came south.
Nobody checked. In a realm where a man's word is his standing, the most effective weapon available turned out to be a well-placed falsehood delivered by a man everyone found useful.
Elsewhere in the wiki
 See the world as it stood in 298 AC What became of it  if an ending is written, it is here. Spoilers.
The chronicle records no ending here ÔÇö or none the maesters have set down.