Having broken free of the Lich King's waning power, Sylvanas had turned down the offer to rule the Plaguelands jointly with Balnazzar, Varimathras and Detheroc, as she considered this simply as another form of slavery. She gathered together a small army of free-willed Undead and defeated Varimathras, forcing him to pledge allegiance to her cause. The two of them marched upon Detheroc and slaughtered both him and his retainers, sparing the life of his mind-slave Grand Marshal Garithos so that he could bolster their forces with his remaining Alliance troops. In return for helping her attack Balnazzar, the last and most powerful Dreadlord, Sylvanas promised the egotistical commander control of Lordaeron.
Balnazzar was no fool; he had reinforced the former human capital extensively after ousting Arthas Menethil, and had gathered a very large Undead army to defend it, as well as opening a Dimensional Gateway to summon Demonic reinforcements. He was outraged by his brother's treachery, and promised to respond to Detheroc's destruction in kind.
The Battle
Sylvanas and Varimathras launched a frontal assault upon Lordaeron's walls whilst Garithos attacked from the rear. The latter was most displeased to find that his Ironforge reinforcements had gotten lost on the way to the battle; Garithos had to fight his way through the wilderness to lead them to safety. Despite the tensions between the racist commander and his Dwarven charges (who didn't think they were getting paid enough), this action added much needed firepower to Garithos's assault and the Alliance began to make headway against the Undead, forcing them back further and further into the city.
Likewise, despite the terrible magical powers Balnazzar brought to bear upon his foes, Sylvanas, Varimathras and Garithos managed to destroy the Loyalists' and Insurgents' bases, claim their resources and defend their own before storming Balnazzar's base with a two-pronged attack from the front and rear before capturing Balnazzar himself.
Aftermath
Sylvanas ordered Varimathras to kill Balnazzar, as a last test of the Dreadlord's loyalty to her. Despite his protests that the Nathrezim were forbidden to harm one another he eventually did so, or at least seemed to. Garithos then ordered them out of "his" city, and Sylvanas told Varimathras to kill him also, which he gladly did with no remorse. The remains of Garithos's forces were slain or fled. With this final victory, Sylvanas declared herself ruler of the Plaguelands, and renamed the free-willed Undead who had pledged themselves to her the Forsaken.
In fact, whether by accident or design Varimathras did not kill Balnazzar; he later resurfaced disguised as the leader of the Scarlet Crusade. Whilst Ras Splinterspine and Morbent Fell were defeated in this battle, they may have survived if their phylacteries remained intact.
Transcript
Varimathras: "The capital city is heavily defended. Balnazaar is no fool, my lady. This battle can be won only through attrition."
Varimathras: "Watch your tongue, human dog. Your hollow bravado does not impress—"
Sylvanas Windrunner: "Stand down, gentlemen! Save your anger for Balnazaar. Garithos, I'll lead my forces in a frontal assault while you attack the city from the rear. Give the order. Let the attack commence."
Grand Marshal Garithos: "An aggressive ploy, milady. So long as we get our capital back, I'll stick to whatever strategy you wish."
Footman: "Lord Garithos, our scouts have found the missing band of dwarves! They appear to be lost in the wilderness nearby."
Grand Marshal Garithos: "Those brainless dwarves are almost more trouble then they're worth! However, we'll need them on the front lines. I'll have to lead them myself."
Grand Marshal Garithos: "Can't you idiots follow simple orders? There's a war on, and you louts are off having a picnic! Get this column rolling immediately!"
Riflemen: "Right away, Lord Garithos! Move 'em out, lads!"
Riflemen: "They don't pay us enough to put up with that asshole."
Quotes in the middle of the battle.
Sylvanas Windrunner: "Let's see. I've made one of your brothers my servant, and tore the other to bloody shreds. I wonder what your fate holds, Balnazzar?"