The idea of seagoing air bases dates back to the first years of heavier-than-air flight, with first shipboard takeoffs and landings around 1910/1911. However, through World War I and at least a decade after, the field seemed to belong to seaplane carriers -- ships that would launch seaplanes with catapults and retrieve them from the sea with cranes after the landing. Seaplane carriers participated in WW1, but did not play an important role.
Aircraft carriers came up between the wars and quickly become the most important surface combatants in World War II. Unlike seaplane carriers, they carried not seaplanes, but special carrier planes designed to start from their flight deck and land there again.
Today, carrier planes are launched by special steam catapults. The large U.S. 'supercarriers' such as those of the Nimitz class can launch their entire air wing of about 80 planes in approximately half an hour. Recovery of the planes is made by having them touch down on an angled deck which is basically a short landing strip running diagonally across the carrier's deck. A tailhook on the plane grabs trap wires slung across the deck and hooked up to what are basically huge recoil brakes.
Planes are moved around on the flight deck by special tractors and transported to and from the hangars below deck by lifts about the size of tennis courts. The planes' wings fold up to save space, because even on a supercarrier longer than 300 metres, the hangars are quite cramped with 80 aeroplanes below deck.
All flight deck operations are coordinated by someone usually called Air Boss, and the flight deck personnel's coveralls are colour-coded by their role in the complicated ballet of launching, recovery, refueling and rearming.
Carriers haven't got railings around their flight decks (duh). If someone goes overboard, chances are the safety netting underneath the flight deck's edges will catch them, though.