This page contains information regarding Star Trek: Strange New Worlds, and thus may contain spoilers.
In 2293, the location of Memory Alpha in the Milky Way Galaxy was labeled in a star chart that was in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country okudagram)
In 2399, the location of Memory Alpha was labeled in a Federation star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. The planetoid was located in or near to Federation space. (PIC: "Maps and Legends")
The Federation built a central library on an unnamed planetoid to hold the total cultural history and scientific knowledge of all planetary Federation members. During assembly, the library wasn't installed with protective shields as this was considered inappropriate for a facility dedicated to academic research.
As of 2269, the library complex was an array consisting of five large and seven smaller domes on the surface of the planetoid. Aside from the technicians, the occupants of Memory Alpha varied with the number of scholars, researchers, and scientists from various Federation planets who were using the computer complex at any given time.
In that year, the USS Enterprise was en route to transfer newly designed equipment to Memory Alpha. Lieutenant Mira Romaine was on her first deep space assignment to supervise the transport from the emergency manual monitor. Before the arrival of the Enterprise, Memory Alpha was attacked by the non-corporeal Zetarians.
While the Zetarians were attempting to take over the bodies of the personnel of Memory Alpha, they managed to cause extensive damage to the complex. The memory core of the computer, called the central brain, was burned out. The energy generator was rendered inoperative. All occupants of the complex died from brain damage caused by resisting the mind control efforts of the Zetarians. After the Zetarians were destroyed, the Enterprise returned to Memory Alpha to begin repairs. (TOS: "The Lights of Zetar")
The name of this facility was originally "Memory 7". The idea that the name be changed was first suggested in a list of research notes submitted by the de Forest Research Company on 16 October 1968. Regarding the designation "Memory 7", the document commented, "This name would imply that there are six other 'Memories.' Since script specifies that installation is unique, suggest: Memory One or Memory Alpha here and throughout script."
According to Michael Okuda, "Based on the size and spacing of the windows, I'd estimate that each of the domes must be similar to the Superdome." He also stated, "If you look very closely at the far left dome, you might notice a small blue patch on the top of the dome. That's the Memory Alpha emblem." 
As evidenced by the first draft script of TNG: "Relics", Memory Alpha was originally to have been cited as the location of the Fleet Museum. However, all mention of Memory Alpha was removed from the episode by the time the final draft of the script was issued. 
A working title of ENT: "The Andorian Incident" was "Assault on Memory Alpha". While the episode was called that, the story included a Vulcan space station named "Memory Alpha". In a story outline, it was described as "a massive data archive that will store hundreds of years worth of scientific data and historical research." The facility was under construction at the time the story was set, with "the last third of the structure" being built by laborers of an alien species who were hired by the Vulcans. Starfleet hoped to someday build a similar archive of their own (implying that the Vulcan station led to the building of the canonically established Memory Alpha). As "The Andorian Incident" continued to develop, this facility was replaced by the Vulcan monastery at P'Jem. However, the term "Memory Alpha" was used even in the episode's first draft script (which had the working title "Incident at P'Jem"), because an underground spy station beneath the monastery (which does appear in the episode) was referred to as that, three times (the first time used in the stage directions, in quotation marks, and the next two appearing in scripted dialogue without quotation marks).
According to Star Trek Maps (p. 27 & chart D), Memory Alpha was established for the Federation Centennial celebration and opened to the general public two years later. The library computer was only partially destroyed by the Zetarians and was overhauled after the attack. The resident population was six hundred. Memory Alpha had a small moon called "Arsende".
According to FASA's The Federation sourcebook, Memory Alpha was the second planet in the Karn Sim system. Decipher's Worlds sourcebook contradicts this, saying that Memory Alpha is the only satellite orbiting its star.
The Memory Alpha facility is mentioned in the 1988 novel sequel to "The Lights of Zetar", Memory Prime. Memory Alpha is also referred to in Boogeymen, and research done at the complex was referenced in Demons of Air and Darkness and Preserver. Memory Alpha is mentioned in Losing the Peace.