Ascent of the Dragons
The Targaryens, descendents of the only survivors of the Doom of Valyria, were based in Dragonstone, a former Valyrian outpost. Having felt forsaken by their own gods, the first Targaryens converted to the dominant religion of the area, the Faith of the Seven.
Aegon the Conqueror left Dragonstone with his wives Rhaenys and Visenya, who were also his sisters. (Inbreeding was regularly practiced in the family, sometimes with tragic results.) The trio landed on Westeros with a small army and Aegon's secret weapon -- the last three remaining dragons in the world. Aegon handily defeated six of the seven kingdoms of Westeros.
The city of King's Landing was established at the place where Aegon first began his conquest and became the family's seat of power. After more than 250 years of Targaryen rule, King Aerys II, known as the "Mad King" took the Iron Throne. His descent into insanity ended violently after an uprising led by Robert Baratheon of Storm's End. Two surviving Targaryen children -- Viserys, regarded by some as the rightful king of the Seven Kingdoms, and his sister Daenerys -- were able to flee to the eastern continent of Essos, where they've grown up in exile.