The Andals cross the narrow sea
They came in waves with iron weapons, seven-pointed stars carved into their flesh, and a new faith that had no use for trees with faces. Kingdom by kingdom the First Men were beaten, married, or converted, until only the North ÔÇö behind its neck of swamp and its stubbornness ÔÇö still kept the old gods. Nearly every noble house south of the Neck counts Andal blood from here.
The fuller tale
The Andals crossed the narrow sea in ships, in waves, over a period the maesters cannot agree on to within four thousand years. Their own account is that the Seven told them to go. The Citadel's account is that they were being pushed from behind by the growth of Valyria, and that men fleeing dragons will tell themselves they were called rather than driven.
They landed in the Vale first and worked outward. What they had that the First Men did not was iron, and what they had that mattered more was a faith with an organisation behind it. Where the sword failed the septons arrived, and where both failed the Andals simply married the daughters of the men they could not beat, which within three generations produced lords who were Andal by blood and First Men by descent and saw no contradiction in it.
The Neck stopped them. Bog, fever, crannogmen who fought from water, and a causeway with Moat Cailin sitting on it: an invading host could take the North only by going through a swamp defended by people who knew it, and none of them managed it. So the line held at the Neck, and it is still there ÔÇö the Faith of the Seven to the south of it, the old gods to the north, the same border eight thousand years later.
The gift nobody credits them for
The Andals brought writing that could carry a sentence. First Men runes could record a name and a claim; Andal script could record an argument, a grievance, a tally, a story. Almost everything in this chronicle before their arrival is a song, and almost everything after it is a document, and the difference is entirely theirs.
They also brought the seven-pointed star, cut into their own flesh on landing, and with it the idea that a faith might have opinions about who should be king ÔÇö a notion the realm would find extremely expensive twice over, once under Maegor and once at the end.
Elsewhere in the wiki
 See the world as it stood in 6,000 BC 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.