The Old Way is a term used by the Ironborn to refer to their traditional lifestyle of reaving and plundering. According to the Old Way, the ironborn raised their Kings from their own numbers. It is also consecrated in the ironborn religion, as they believe the Drowned God made them to reap and rape, to carve out kingdoms to make their names known in blood and song.
The Old Way centers around the concept of "paying the iron price": to seize any wealth or possession by force. To pay the "gold price" is shameful for any man.
Another aspect of the Old Way is that ironborn are not expected to farm, work the land, or toll in mines; such tasks are reserved for thralls: men and women captured in raids and forced into servitude. If a woman is considered attractive, she's made into a salt wife, a bound concubine.
Following the Old Way, the ironborn carved a kingdom that came to dominate much of the western coast of Westeros, going as far east as the Trident and its surrounding lands. However, when Aegon I Targaryen conquered Westeros, he outlawed the Old Way and restored the Riverlands to its people.
Three hundred years later, Balon Greyjoy declared himself King of the Iron Islands and rebelled against the Iron Throne in an attempt to revive the Old Way but was soundly defeated and forced to bend the knee. More than a decade later, with the Seven Kingdoms embroiled in civil war, Lord Balon once again declared himself King and revived the Old Way to seize the North.
In the books
In the A Song of Ice and Fire novels, following the Old Way once led the ironborn to rule much of the western coast of Westeros, from Bear Island to the Arbor, though they lost much of their territory in war against the neighboring kingdoms. Aegon the Conqueror outlawed the Old Way, forcing the ironborn to raid outside the realm - though minor attacks against the Western coast of the North were still carried out. During the rule of Aerys I Targaryen, Lord Dagon Greyjoy revived the Old Way and the ironborn raided as far south as the Arbor and even the North, as the Iron Throne was preoccupied with the Blackfyre pretenders across the Narrow Sea and the Great Spring Sickness