Since we're dealing with a tetralogy of novels, there's one big story arc that follows the typical plot structure, but each book also has its very own crises and turning points.
Exposition (Initial Situation)
They Don't Call It "The Dark Ages" for Nothing
The Sword in the Stone eases us into the story by giving us the gist of the general situation in England. Uther Pendragon is king, and he's basically a tyrant (lite). Plus, there are a lot of violent barons who have no regard at all for the poor people. In fact, the entire country is pretty much under the rule of the strongest: those who have the Might are automatically Right.
At the very end of the opening book, we learn that our little guy Wart is actually Uther's son. So he's heir to the throne of England, which he demonstrates by drawing a magical sword from the famous stone. Who'd have seen it coming—this guy is so low on the totem pole that he's nicknamed after a nasty foot growth.
Rising Action (Conflict, Complication)
Arthur: An Enlightened Leader
The Queen of Air and Darkness continues to work through the whole Might is Right issue. Just because Arthur is now king doesn't mean that all of these issues magically disappear. Even Merlyn can't make that happen. More conflict enters the picture when King Lot and the Gaelic Federation refuse Arthur's rule, and he has to rally his troops for one more major battle… until Lot surrenders.
But tyranny still refuses to depart Gramarye. To combat this, Arthur gets the idea to create a Round Table—a group of knights who will channel their aggressive tendencies into enforcing justice and maintaining peace. Bringing together these 150 knights sets the stage for some of the plot complications that arise in the next two novels.
One major family feud between the Pellinores and the Orkneys develops over the course of The Queen of Air and Darkness and The Ill-Fated Knight, and ultimately leads to multiple deaths.
Sins Coming Home to Roost
The climactic point in The Queen of Air and Darkness gives us one major point of conflict that will have serious repercussions throughout the rest of the books: Morgause seduces Arthur, and the two sleep together. Oh yeah: did we mention that they're related? Incest is a big no-no, naturally.
Mordred is the child that results from this sinful union. Because Arthur tries to kill him (murdering many innocent babies in the process), Mordred bears an everlasting grudge toward his father (there's a shocker!) and will eventually ensure that Arthur's sins—no matter how accidental or inept—will come back to haunt him.
I Love You. Now Go Away.
Greatly complicating the web of conflicts already stickying up Arthur's Round Table is the adulterous affair between Guenever and Lancelot that has been going on for years. This makes up the central narrative arc of The Ill-Made Knight, and a big chunk of The Candle in the Wind.
This relationship puts Lancelot at odds with the other knights, and puts Arthur in the awkward position of having to put his own wife on trial twice during the rising action of the novels: because of Sir Pinel's accusation against Guenever for poisoning Sir Patrick, and Sir Meliagrance's charge of adultery against the Queen. Lucky, the ever-heroic Lancelot rescues her both times.
Climax (Crisis, Turning Point)
Well, at Least It's Out in the Open?
The climax of the entire series is in The Candle in the Wind, when Agravaine, Mordred, and eleven other knights lie in wait for Lancelot to sneak into the Queen's bedchamber. As long as the affair was not recognized publicly, Arthur did not have to act.
Now, though, it's all out in the open, and he has no choice but to put Guenever on trial once again. If Lancelot doesn't rescue her, she'll burn at the stake. Good ol' Lance does his heroic thing, and then there's a big war between Arthur and Lancelot… which is only stopped when the Pope makes them knock it off (in a clever plan designed by Lance). Guenever is returned to Arthur in a ginormous and formal ceremony.
The King Is Dead. Long Live the King!
But that's not quite the end of that episode. Gawain just can't forget that Lancelot killed his two innocent, unarmed brothers (Gareth and Gaheris), and finally succeeds in cajoling his Uncle Art into having another go at Lancelot.
So, the English army sails off to fight the Frenchman on his own turf. Meanwhile, Mordred (who has not stopped hating his father) sees this as an opportunity to tell the English people that Arthur's dead...and has been killed by Lancelot.
So Mordred's now king. Plus, he'll take Guenever for his Queen, thankyouverymuch. Might as well continue the pattern of inappropriate familial relationships, right?
Turning Things Over to Tom
At the very end of The Candle in the Wind, we find out that Gawain has died from the wounds Lancelot gave him (which were, strangely enough, on the same exact spot on his noggin as the wounds Galahad gave him during the Grail Quest). But, before he can die, he sends off a letter to Lance, telling him to come help Arthur fight Mordred.
The book ends with Arthur in his royal pavilion, thinking back over all the lessons he's learned about Might and war, and how people just haven't yet evolved enough to not be warlike. He tells his story to a page, Tom Malory, and asks that he keep this knowledge and pass it down through the generations.
Then he goes off to his destiny—either to die, or to be taken to the island of Avilion.