How did they replace destroyed planes on WW2 aircraft carriers?

Although practice about replacement aircraft differed between navies, there were several methods for replacing damaged or lost aircraft. The most common method was to keep a number of replacement aircraft in storage on the larger fleet carriers. These aircraft were disassembled and required a number of man-hours to put back together. In the USN, starting with USS Ranger, carrier designs to incorporate enough space to stow aircraft in the ceiling of the hangar, as seen in this photo from Friedman's US Aircraft Carriers. The earlier IJN carriers tended to keep their reserve aircraft in a disassembled state in their lower hangars. The British also adapted a similiar strategy of stowing disassembled aircraft. During the war, fitters and crewmen would assemble these stowed aircraft to meet the needs of operations. For the Pearl Harbor operation, Zuikaku's crew assembled its three A6Ms to act as a CAP for the fleet given the needs of the strike force had absorbed up most of the fighters of Kido Butai.

Yet the growing size and complexity of naval aircraft in the 1940s made this stratagem more problematic. One solution was to plan for carriers t field a larger number of fully functional aircraft that exceeded the number of pilots in their attached airgroup. Staring with Soryu, the Japanese planned to keep a number of excess aircraft in readiness so that they could be used as replacements in very little time. however, the persistent shortfalls of the Japanese aviation industry meant that Japanese carriers often went to sea with an understrength airwing. At Midway, Kido Butai parted out a number of these spare operational aircraft to other carriers, denuding the IJN's main strike force of a reserve. The USN's Essex class, USN fleet carriers started to field a reserve squadron of aircraft kept in near operational readiness. While the Navy Board initially envisioned a homogeneous reserve squadron, wartime experience led to a heterogeneous and truncated squadron of each aircraft type (dive/scout bomber, fighter, torpedo). Although USN investment in wing-folding technology helped ease the concerns of space, such a situation created a cramped hangar even on the the large Essex class ships. One solution to this problem, and one the US was able to employ because of its large industrial base, was to have a flotilla of smaller escort carriers carry reserve planes and pilots. These "jeep" carriers would supplement the aviation operations of the task force, but also serve as ferries for aircraft to either the carriers or newly captured bases in the Pacific. The British hit upon a similiar idea, but economized it with HMS Unicorn, which was a small fleet carrier designed to be an aviation depot ship. She had various machine shops and excess spare parts for the fleets' damaged aircraft. She carried spare aircraft and a modest complement of self-defense fighters, but was mostly designed for operation at harbors, especially those without advanced fleet facilities. She had cranes and aircraft lighters for ferrying unserviceable aircraft and her flight deck allowed repaired aircraft to take off and return to their ship.

edit: tidied up language and added a little about the wartime IJN