What happens in Canto XII of Dante's Inferno?

Canto XII
Forewarned by Virgil of the horrors to come, Dante and his guide leave the flaming tombs of the arch-Heretics behind them. The path to the first of the lowest circles is incredibly steep. As Dante treads carefully, he compares the rough terrain to the infamous landslides of Marco, a city in northern Italy, near Trent.

"The place where to descend the bank we came
Was alpine, and from what was there, moreover,
Of such a kind that every eye would shun it.
Such as that ruin is which in the flank
Smote, on this side of Trent, the Adige,
Either by earthquake or by failing stay,
For from the mountain's top, from which it moved,
Unto the plain the cliff is shattered so,
Some path 'twould give to him who was above..."

The landing proves even more terrifying than the descent. At the bottom stands the enormous Minotaur, a monster with the head of a bull and the body of a man. The Minotaur spies the invaders and becomes enraged, so much so that he confusedly take his anger out on himself, biting his own arm in fury.
Virgil knows the monster believes that the intruder of his domain to be Theseus, the Duke of Athens (Theseus had slain the Minotaur on Earth). Virgil both rebukes and taunts the beast. He tells him not only to back down, but also that he and Dante are in Hell, in part, to enjoy watching him suffer. Virgil calls out:

“Peradventure
Thou think'st that here may be the Duke of Athens,
Who in the world above brought death to thee?
Get thee gone, beast, for this one cometh not
Instructed by thy sister, but he comes
In order to behold your punishments."

The gibes enrage the monster even more and goes in pursuit of the intruders. Virgil urges Dante out of his stumbling reach, crying,

“Run to the passage;
While he wroth, 'tis well thou shouldst descend."

Having evaded the Minotaur, the travelers’ challenges are far from over. The rubble underfoot is treacherous. Virgil explains to Dante how the upheaval came about. On Virgil’s previous journey into Hell, he witnessed the rapture of the good men who had died prior to Jesus’s salvation of the damned. The force of Christ’s love shook the universe, even to the depths of Hell. Virgil explains:

“... a little
Before His coming who the mighty spoil
Bore off from Dis, in the supernal circle,
Upon all sides the deep and loathsome valley
Trembled so, that I thought the Universe
Was thrilled with love, by which there are who think
The world ofttimes converted into chaos;
And at that moment this primeval crag
Both here and elsewhere made such overthrow.”

As Virgil concludes his story, the pair find themselves at an impasse. They have reached a river of boiling blood; its name is “Phlegethon.” Dante is terrified to see that the banks are thick with an army of centaurs, monsters that are half man, half horse. These guardians are armed with bows and arrows. One of their legion cries out to Virgil, demanding to know:

“Unto what torment
Come ye, who down the hillside are descending?”

Virgil refuses to answer, saying he will only speak to Chiron, the leader of the centaurs. Surrounded by the herd but continuing to move forward, Virgil points out two individuals among the armed sentries: Nessus, and the leader of the pack, Chiron.
The centaur Nessus was slain by Hercules, who, in turn, was killed by the beast’s poisoned blood. Dejanira’s name in Greek means “man destroyer.” Dejanria was Hercules’s wife. Nessus attempted to rape her and was shot by an arrow launched by Heracles in the attempt. As the centaur lay dying, he gave the woman a cloak soaked in his blood. Nessus claimed that the cloak would preserve Dejanira’s love for Heracles; the grieving wife took the garment to her dying husband, but Nessus had deceived her. The blood was poisonous and he died. (In despair, Dejarina hung herself, thereby committing the mortal sin of suicide.)
Chiron, even though he is condemned, has a more laudable reputation. In life, the centaur had been a tutor to both Hercules and Achilles. He acts as the guardian to Circle Seven.
Eyeing the pair as they come closer, Chiron tells his army to watch out for Dante, as the intruder, unlike Virgil, who is a shade, can actually alter the physical environment. Chiron warns:

“Are you ware
That he behind moveth whate'er he touches?
Thus are not wont to do the feet of dead men."

Virgil tells the centaur that Dante indeed is alive. He explains that he and his charge are on a mission from God and asks that Chiron not only allow passage, but also permit one of the herd to accompany them and carry Dante over the river of blood:

"Indeed he lives, and thus alone
Me it behoves to show him the dark valley;
Necessity, and not delight, impels us.
Some one withdrew from singing Halleluja,
Who unto me committed this new office;
No thief is he, nor I a thievish spirit.
But by that virtue through which I am moving
My steps along this savage thoroughfare,
Give us some one of thine, to be with us,
And who may show us where to pass the ford,
And who may carry this one on his back;
For 'tis no spirit that can walk the air."

Chiron understands and selects Nessus to be their emissary through the circle. Dante climbs on the beast’s back. The trio proceed and Nessus points out some of the tormented souls in the boiling river of blood:

"Tyrants are these,
Who dealt in bloodshed and in pillaging.
Here they lament their pitiless mischiefs; here
Is Alexander, and fierce Dionysius
Who upon Sicily brought dolorous years.
That forehead there which has the hair so black
Is Azzolin; and the other who is blond,
Obizzo is of Esti, who, in truth,
Up in the world was by his stepson slain."

All of these men had committed mass acts of violence against entire populations. Alexander is almost definitely Alexander the Great, the military conqueror, whose bloody coup of Persia ousted King Darius III. Dionysus was held in contempt by the ancient philosophers, not only for his bloody murders but also for his thirst for revenge and greed. Azzolin (also known as “Azzolinao” as well as “Ezzelino”) was a feudal Italian lord who was regarded as a cruel tyrant who ruled Verona, Vincenza, and Pauda. Obizzo d’Este is placed in Hell by Dante for his crime of buying a woman from her brother in order to rape her.
Still astride Nessus’s back, the three continue on. They stop in order for centaur to point out Guy de Montfort, who led a rebellion against King Henry III. De Montfort and his brother Simon murdered Henry III at the Church of San Silvestro, taking no mercy on the monarch who clung to the altar and begged for his life. As Dante watches the man’s torment, he realizes that the depth of the river changes in direct correlation to the seriousness of the sinner’s crimes:

"Then people saw I, who from out the river
Lifted their heads and also all the chest;
And many among these I recognised.
Thus ever more and more grew shallower
That blood, so that the feet alone it covered;
And there across the moat our passage was."

Nessus carries Dante across at the lowest point and Virgil follows. The centaur tells the poet that as the river winds lower into the depths of Hell, the waters will become deeper still; in these boiling depths Dante and Virgil will find Attila, Pyrrhus, and Sextus.
Attila (frequently called “Attila the Hun”) was the great enemy of the Roman Empire, plundering the Balkans, and, along with his armies, left a trail of corpses from Persia to France to Rome. Pyrrhus was regarded by Dante (and others) as a tyrant for his bloody battles in opposition to Rome. For his part, Sextus, or “Sextus Pompey,” is the son of Gnaeus Pompeius Magnus, (also known as “Pompey the Great"). Sextus is condemned to Hell’s Seventh Circle for his opposition to the Second Triumvirate, the political alliance between Augustus (who had once been known as “Octavian”), Marc Antony, and Marcus Aemilius Lepidus.
Now safely across, Nessus takes his leave of Virgil and Dante. The poets carry on alone.