From A Wiki of Ice and Fire
The Old Way is a term used by the ironborn when discussing their ancient tradition of reaving and plunder. Acquiring items through battle instead of purchase is referred to as paying the iron price. Before the War of Conquest, the ironborn would use lightning raids from the sea to carry away women and plunder and burn what they left behind. Using this method they carved a great kingdom out of the riverlands, though their ships were known from the Free Cities to the southern coasts of Westeros near Oldtown. When attacking castles, ironborn are not to fling rocks or starve out a foe, but rather they should storm the fortress with grapnel and ladder.
During the War of Conquest, Aegon the Conqueror pacified the ironborn and outlawed the custom, at least within Westeros, as the ironmen were allowed to prey on the shipping and settlements of the Free Cities and far away places. Those that continue to act in such a manner are said to be keeping to the Old Way.