Drowned Men are initiated by being "drowned" a second time, this time for real by being forcibly held under the waves by initiated priests. After their lungs fill up with water and they stop moving, they are brought back to shore, and revived by a priest using a crude form of cardiopulmonary resuscitation. If he is successfully revived, the gathered Drowned Men welcome their new brother to the clergy. Traditionally, they arm and clothe themselves only with what the sea washes ashore.
Known Drowned Men
In the books
In the A Song of Ice and Fire novels, the Drowned Men carry cudgels of driftwood. They are forbidden from shedding the blood of other ironborn, but this restriction is taken quite literally: they are still permitted to bludgeon enemies to death with driftwood clubs. It is also quite praiseworthy to drown an offending ironborn, as a sacrifice to the Drowned God.
New initiates to the Drowned Men are literally drowned by a current member of the order (similarly to a baptism ceremony), then revived using a crude form of CPR. The Drowned Men are not always successful in reviving adherents, however, and a Drowned Man is considered to be very holy indeed if he has failed to revive only one or two men who undergo the ceremony in his career. Aeron Greyjoy takes pride of the fact that he has never lost a man he baptized.
The Drowned Men priesthood have no hierarchical organization. However, prestige, time as a Drowned Man, and the number of initiates successfully resuscitated do grant particular Drowned Men a level of authority. At the time of the War of the Five Kings, Aeron "Damphair" Greyjoy is universally held to be the leader of the Drowned Men, who obey his orders without question. He commands great respect from all of the ironborn. However, Aeron wasn't appointed as some kind of high priest; rather he rose to a position of primus inter pares through general acclamation.