The Library Computer Access and Retrieval System (LCARS for short) was the main computer system employed by the United Federation of Planets by the mid-24th century. It was used aboard all Starfleet vessels, starbases, and space stations. (Star Trek: The Next Generation, Star Trek: Deep Space Nine, Star Trek: Voyager, Star Trek: Picard)
LCARS was accessible virtually anywhere in a facility or starship by both voice and keypad commands via control interfaces. These interfaces included bridge stations, consoles, PADDs, tricorders, and desk computers. Typically, these were graphical controls housed underneath touch-sensitive clear panels that could be quickly reconfigured by users to suit the task at hand. There were also tactile interfaces for visually-impaired officers. (TNG: "Encounter at Farpoint", "The Vengeance Factor", "The Host", "Half a Life"; VOY: "Year of Hell")
By 2399, Starfleet had begun deploying three-dimensional holographic interfaces for the LCARS system aboard Federation starships and installations. Civilian craft such as La Sirena also had access to this technology. (Star Trek: Picard)
LCARS used sophisticated subroutines in order to understand and execute vocal natural language commands. This enabled even complicated tasks to be executed with just a few commands in the case of voice or button presses in the case of keypad commands. LCARS controlled the retrieval and storage of files in the data banks housed within the ship's computer cores including logs like personal logs or transporter logs, element and chemical compound data and data on archaeological artifacts. (TNG: "Contagion", "Dark Page", "Man of the People", "Night Terrors", "Qpid") It was used to retrieve files in external databases like when a ship needs to assess traffic control around starbases or investigate inventory databases of surplus depots. (TNG: "Birthright, Part II", "Unification I") It was also used for command system access and for viewing the crew manifest. (TNG: "Brothers", "Conundrum") It was also used to display recently recorded data like medical scans, tactical scans and sensor scans. (TNG: "Ethics", "Interface", "Descent", "Relics", "Genesis") It displayed results of analyses like linguistic analyses, configuration analyses of system networks, and magnetic flux density analyses. (TNG: "Masks", "Attached", "Power Play")
LCARS retained the same basic layout and design across Federation starships and installations, however, a few variations in the color schemes can be noticed.
During normal operations, LCARS color schemes can alternate between a wide ranges of colors, such as tans, purples, and yellows, in addition to blues, aquas, and oranges. (Star Trek: The Next Generation, Star Trek: Deep Space Nine, Star Trek: Voyager, Star Trek: Picard)
During emergencies or special operations, LCARS color schemes are updated to reflect the current alert status, such as Red or Blue alerts. When these alerts are called, LCARS interfaces will switch to either a red/white or blue/white scheme respectively. (Star Trek: Deep Space Nine, Star Trek: Voyager, Star Trek Generations, Star Trek: First Contact, Star Trek Nemesis)
LCARS interfaces are seen in almost every episode of Star Trek: The Next Generation, Star Trek: Deep Space Nine, and Star Trek: Voyager. The interfaces seen in Star Trek: The Original Series are never named and their designs are quite different.
A close-up view of one of the science stations aboard the Enterprise-D in "The Vengeance Factor" has the label "Library Computer Subsystems".  The full name "Library Computer Access and Retrieval System" can be seen in several episodes, including "The Price", "The Measure Of A Man" and "Conundrum". The phrase "library computer access and retrieval" is spoken in "Encounter at Farpoint")
The sickbay used in Star Trek V: The Final Frontier is a minor redress of the TNG sickbay, and the LCARS panels on the wall are barely altered, so this could be the first LCARS appearance. They also appear in Star Trek VI: The Undiscovered Country just below the warp core, but they do not appear in the 23rd century portion of Star Trek Generations.
According to a Next Generation episode text commentary by Michael and Denise Okuda, the LCARS displays were rarely actual computer simulations; one such example was the computer screen used by Romulan Commander Sela to monitor the Federation fleet during her attempt to smuggle weapons and supplies to Lursa and B'Etor during the Klingon civil war in the episode "Redemption II". This was due, according to the Okudas, to both the high cost and primitive state of computer graphics in the late 1980s and early 1990s. Therefore, most LCARS displays were, in fact, plastic panels with spinning light devices behind them to give the impression that the information on the "displays" was changing.
In the first two seasons of The Next Generation, large black rectangles are clearly visible on the LCARS displays on the bridge (and sometimes in main engineering). This was a result of the studio lights reflecting off the displays, which director of photography Edward R. Brown tried to solve by sticking cardboard onto them. When Brown was replaced by Marvin V. Rush for the third season, a number of changes in filming (including better film stock and a smaller number of lights) allowed the LCARS displays to be seen properly. 
The LCARS layout has been used in several computer games and applications such as the CD-ROM version of the Star Trek Encyclopedia, as well as the TNG and DS9 CD-ROM Companions. The LCARS layout is also used on the Star Trek PADD app for the Apple iPad.