(written from a Production point of view)
A near-omnipotent entity from another dimensional plane (resembling an interdimensional Rura Penthe in appearance as well as climate), 0 (zero) was discovered by Q. Q had requested of the Guardian of Forever to be shown "something new, something different." Upon this request, the Guardian displayed various images and events, Q picking one at random.
At their initial meeting, 0 appeared to be a shabby but intricately dressed mischievous n'er-do-well – a facade that reflected none-too-accurately his true appearance and nature; an exiled and partially crippled (he could no longer travel at warp speeds under his own power) entity of formidable power, intellect, and as became evident rather quickly, evil.
Upon Q's invitation to his "home" universe, 0 encountered a setback – The Guardian, recognizing that 0 did not belong on that plane, attempted to restrain 0 and prevent him from crossing the "border" from his exile plane to the universe beyond. Q however, not yet aware of the disastrous outcome of his actions, viewed the Guardian as little more than a "pompous piece of rock", and he pulled 0 through the barrier and into our universe.
Their first port of call was the Q Continuum, although the other Q were more than slightly apprehensive at the arrival of this mysterious, powerful entity, one who did not belong. Q was charged with being 0's "keeper", and vouched for him, believing that it was safe to accept responsibility for 0's actions forthwith. Exiting the Continuum, Q began taking 0 for a tour of our universe, oblivious to the entity's true intentions.
Before long, they both encountered the Calamarain, who at that point in time were known as the Coulalakritous. After observing them for several minutes, 0 declared that he would "use" them as transport, and attempted to restrain them. The Coulalakritous, being none too impressed with this attempt, forcibly ejected both Q and 0 from their group (they had changed form to blend in with their impromptu peers). Enraged, 0 compressed the gaseous entity to the point of being a slush, then ice, and attempted to compress them further (perhaps to create a singularity out of the unfortunate entities' forms). Q stepped in at this point, calling an end to the torture (and in the process bore the brunt of 0's fury for a brief moment). 0 apologized, pleading momentary frustration and Q accepted, albeit cautiously.
Returning to the Guardian's planet, 0 called forth his three "friends and contemporaries", similar entities with malevolent purposes: (*) (encountered by Starfleet at Beta XII-A), Gorgan (later responsible for a series of murders of the old by the young, witnessed and stopped by Captain Kirk) and The One (later encountered by Kirk at the center of the galaxy).
0 goaded Q into trying his hand at "testing lesser species" (in fact he was likely the person responsible for instilling this desire into Q in the first place), a task that Q took to with relish, albeit immature relish – he was responsible for a planet-wide shower of fruit on one of the main planets in the Tkon Empire. 0, however, had other plans for the Tkon; he began manipulating their culture, their technology, their entire way of life, all to his own ends, the end result being a massive civil war in the Tkon's home system between Tkon and an outer-system planet, Rzom. But even in the face of such unrelenting adversity, the Tkon fought back – and nearly won – so 0 pulled his trump card, and in an act of almost unparalleled sadism, caused their sun (which was in its last legs of life) to go supernova only seconds before it was to be replaced with a new, fresh sun (courtesy of an advanced transporter grid, one that present-Q advised Jean-Luc Picard to find before someone else did). This act alone demonstrated how different he was from Q; even when it meant that he might not win, Q always gave lesser lifeforms a chance at success. 0 simply changed the rules completely when it seemed like the Tkon Empire might triumph over him.
This act, the ultimate in a series of distasteful ones, caught the full undivided attention of the Q Continuum. They declared war upon 0 and his compatriots, pitting four against four (the rest of the Continuum being occupied with controlling the side-effects of the crisis) – 0, (*), Gorgan, and The One versus Quinn, Q2, female Q, and the Quaestor. Q was pushed to the sidelines, where he observed the proceedings in anguished regret. The ultimate end to this battle was eventually decided by Q himself who, after defending the Female Q from an almost-fatal attack from 0, stepped in to protect the Quaestor at the pivotal moment. This act not only momentarily shelved 0's powers, it drove him over the edge, into pure unbridled insanity.
Among the casualties of the war were Sargon's species, who turned on each other under (*)'s influence, eventually destroying the atmosphere of their planet; the species who created the android Ruk (The One was responsible for siphoning energy from their sun to use in his fight against the Q); and Earth (0 used an asteroid like a bullet against the female Q; Q knocked her out of the way, then avoided the bullet by "tearing a hole in space-time" which the asteroid flew into, emerging around 65,000,000 BC and slamming into Earth).
After all was over, a court of Q was called into session. (*) (who later fled into space and was trapped forever in a space rift) and Gorgan (who later dissolved into nothingness) had already escaped into the black hole that existed where the Tkon sun once was, but The One and 0 remained. The One, who had been dismembered and depowered by the Q, was banished to the center of the galaxy (later destroyed in Star Trek V: The Final Frontier), and 0 was eternally banished from the Milky Way; the galactic barrier was erected to prevent his re-entry. Q was charged with watching over the primordial Earth because of the damage done by the asteroid.
0 regained entry to our galaxy briefly, when a Betazoid scientist, Dr. Lem Faal, perfected Dr. Lenara Kahn's wormhole technology. A piece of 0's consciousness slipped through a crack in the barrier created during the Q Civil War and joined with Faal, promising him immortality after providing him with subtle hints as to how to penetrate the barrier; Faal, suffering from Iverson's Disease and eager to make his mark on the universe, gladly accepted. After attacking the USS Enterprise-E (by this point, after 600,000 years in exile, he was completely and irreparably insane, not even recognizing the basic underpinnings of reality, a situation which, curiously, then apparently gave him near-unlimited power over existence surpassing even the Q) and killing a Deltan helm officer, he focused his attack upon Q, who was on board the Enterprise, wounding him almost to the point of death.
However, at the last minute, Q was saved when the Calamarain, who had been attacking the Enterprise-E in an attempt to prevent the wormhole experiment, were contacted by Captain Picard, who invited them onto the Enterprise to help fight 0. On Picard's advice, the Calamarain merged with Q after Angosian security officer Baeta Leyoro was killed extracting them from a crystalline lattice into which 0 had compressed them. Their differences set aside, Q and the Calamarain became a single consummate entity, two infinite powers combining to become more than the infinite. Unable to match this unexpected new foe, 0 was easily beaten and re-exiled to the void, any weaknesses in the barrier repaired, and the whole barrier reinforced. It is presumed he remains there as of the late 24th century, as insane as ever, uncertain whether he was ever even freed in the first place. (Q Continuum)
(*) was the true name of the Beta XII-A entity. (Q Continuum; "Night of the Vulture") The entity also appeared in "Night of the Vulture", a short story also written by Cox, featured in Tales of the Dominion War. The entity delighted in the carnage of the Dominion War but unwittingly saved the Federation and Klingons when its machinations killed the crew of a Dominion ship en route to Terok Nor with the codes that would deactivate the minefield guarding the Bajoran wormhole. The entity then became permanently imprisoned in a spatial rift.
One of these was the Q Continuum member later known as Quinn by crew members of the USS Voyager. Other members of the Q Continuum who assisted the Quaestor in battle were the Female Q who later appeared on board the USS Voyager and the Q known as Q2. Q2 was responsible for restoring Q's powers on stardate 43539.1.