Anybody can find their way nowadays with GPS, even back to a carrier far at sea, never having caught sight of land. It took considerably more skill in World War II, although the naval aviator was provided with electronic tools to do so.
For more on each of these tools, see http://tailspintopics.blogspot.com/2014/01/world-war-ii-navy-carrier-airplane.html
However, if all else (or simply the electricity) failed, the pilot had a fallback, his plotting board. (The pilot also needed to be sure that he didn't fly farther from the carrier than he had fuel for the return; none of his electronic aids provided that information.)
It was removable, like a kitchen drawer, sliding in and out of a slot in the lower side of the instrument panel.
A circular slide rule, fondly known as a whiz wheel, was mounted in the lower right-hand corner of the plotting board. This was used to calculate ground speed, fuel burn, etc. The big circular grid was used to plot the carrier's projected track and the airplane's actual track. A plastic cover allowed the pilot to mark on the board and erase it for subsequent use.
Before takeoff, the pilots would be briefed on the carrier's intended course and speed and the forecast wind aloft at various altitudes. Since missions might last three hours or more, the carrier might be long gone and out of sight relative to its position at takeoff. Wind aloft was also critical because airplanes, like balloons, drift with the wind and do not necessarily go in the direction that they are headed or at the speed being flown through the air.
After takeoff, the pilot could resort to the same navigation technique of captains on sailing ships in centuries past, keeping close track of airspeed, heading, and time at the different speeds and heading, the manual equivalent of an inertial navigation system. Wind aloft then had to be factored in to determine the ground speed, track, and distance made good. (Pilots were taught how to estimate the strength and direction of the wind from various clues like the appearance of the waves.)
The result was a continuous record of the approximate position of the airplane relative to that of the aircraft carrier. When the time came to return, a course back to home plate could quickly be determined.
Of course, the pilot might not know exactly where he had been, since a lot of maneuvering might have been involved so his plot was not complete or accurate, the wind might have been different from forecast and checking it not possible, etc. The carrier also might not have made good its intended plan of movement. So if the carrier was not in sight when he got to where he thought it was, he would execute an expanding square search.
The Brits considered the workload and degree of difficulty in finding the way back to the carrier to be so high that their front-line fighter at the start of World War II, the Fairey Fulmar, had a two-man crew, pilot and navigator.
On or about the time that jets were introduced, the plotting boards were removed and no longer required in favor of knee boards and presumably an increased reliance on the electronic aids.