Quel'Serrar was not a legendary weapon like Thunderfury or Sulfuras, but it was almost as rare. Unlike the Bindings of the Windseeker or the Eye of Sulfuras, the item required to begin the chain was BoE. This meant that very, very rarely you could find the item on the Auction House -- but if you did happen to be so lucky, you'd pay an arm and a leg for it. Only warriors and paladins could accept the quest for the blade, but the book would drop for anyone who was lucky enough to find it in the corridors of Dire Maul.
As a blade of legend, Quel'Serrar was forged in a special ceremony with the "children of the Aspects" -- not the Aspects themselves, but the dragons of their various flights. It was rare to see a Quel'Serrar forged, for not only would a dragon have to heat and mold the metal of the blade with their breath, they would also have to temper the blade with their blood ... and it was highly unlikely a dragon would care to do such a thing.
Over the course of thousands of years, only a handful of these blades were created for the kal'dorei, each unique in appearance and power. According to Lorekeeper Lydros, each blade would take on the appearance of their creator, which may mean that the blade's appearance changed depending on which flight happened to create it. But Lorekeeper Lydros didn't just keep the story of the blade; he also kept a remnant of Quel'Serrar, hidden safely within the inner sanctum of Dire Maul.
If the noble warrior or paladin were brave enough to face Onyxia in her lair, they could place the Unfired Ancient Blade in front of Onyxia, in the path of her flaming breath. And once Onyxia was defeated, the Heated Ancient Blade had to be thrust into her heart, tempering the blade with her blood. This had to be done quickly, however -- waiting too long would ruin the blade. Once completed, returning to Lorekeeper Lydros with the Treated Ancient Blade would allow him to complete the ceremony and hand over Quel'Serrar in all its shining glory.
Quel'Serrar is one of the few weapons in the world that actually have multiple copies according to lore. Even though Lorekeeper Lydros claimed only a handful were created, it's possible he has plenty of those Dull and Flat Elven Blades lying around. It's simply a matter of finding a dragon to assist in creating the blade. But far more curious than Lorekeeper Lydros' blades are his tales of a more powerful Quel'Serrar than the one the player creates.
Regardless, those that were successful in their attempt to gain a Quel'Serrar are a proud group who defeated a dragon when she was at her most powerful. When Onyxia received her level 80 update in Wrath of the Lich King, the path to obtain a Quel'Serrar was wiped from WoW. Unfortunately, the only way to obtain a Quel'Serrar nowadays is to loot one from Onyxia's corpse, a far less prestigious accomplishment.
There are still those who wield the original blade, but their numbers are far fewer than those who wield the Gleaming or Burnished versions you can obtain today. And for those warriors and paladins who wield the original, they look back on those days as a fond memory, when might and bravery won them a treasure beyond compare, started by stumbling upon a battered and dusty book.
For more reading, take a look at Know Your Lore's history of the Shen'dralar and the dragonflights.