We first meet Patroklos in Book 1. After fighting with Agamemnon, Achilleus goes back to his shelter to hang out with Patroklos and wait for Agamemnon's heralds to come take away Briseis.
We see him again in Book 9, when he is, once again, chilling out with Achilleus, who is playing the lyre.
Then, flash forward to Book 11, when Achilleus, who is watching the battle from the stern of his beached ship, calls Patroklos out of the shelter to go check on the identity of Machaon, whom he thinks he sees being driven back to the ships in Nestor's chariot.
Patroklos obeys, thus sealing his doom.
When Patroklos gets to where Nestor and Machaon are and confirms the injured man's identity, he turns to go.
But Nestor holds him back, and tells him how bad things are going for the Achaians. He reminds Patroklos about the day he and Odysseus came to the house of Peleus looking for recruits. At the time, he and his playmate Achilleus were eager to join the expedition.
Then Nestor reminds him of how Patroklos's father, Menoitios, told him that his role was to give advice to Achilleus.
Now Nestor gets to the point. He suggests that Patroklos should lead the Myrmidons, wearing Achilleus's armor.
Patroklos is thrilled by this suggestion, and runs off to find Achilleus.
Along the way, he encounters the Achaian warrior Eurypylos, who has been injured by an arrow.
Eurypylos gives Patroklos even more of the bad news on how they're doing.
Patroklos helps Eurypylos back to his tent and removes the arrow.
When Patroklos sees that the Trojans have pushed the Achaians back upon their own ships, he leaves the injured man and runs off to find Achilleus.
By the time he reaches Achilleus, he is in tears.
Achilleus makes fun of him for crying, but Patroklos defends himself. He tells off Achilleus for being a jerk, and asks for permission to lead the Myrmidons into battle.
Achilleus agrees, and tells Patroklos to take his armor. The only condition he imposes is that Patroklos should only drive the Trojans off the ships. "Don't go any further," he says, "or you'll make me look stupid."
When Achilleus sees one of the Achaian ships getting burned, he tells Patroklos to start moving.
Patroklos arms himself in Achilleus's gear, taking everything except his spear, which only Achilleus is strong enough to wield effectively.
Patroklos leads the Myrmidons out to battle. The Trojans are stuck with terror, thinking it is Achilleus. They are driven back.
In the battle that follows, Patroklos kills numerous dudes.
When Sarpedon sees this, he tells off his fellow Lykians for not standing up to Patroklos. He decides to take him on himself.
Patroklos throws his spear and kills Sarpedon's chariot driver.
Sarpedon then kills Patroklos's horse. When Sarpedon throws his second spear, however, he misses.
Patroklos's second spear hits Sarpedon in the heart, mortally wounding him.
After Zeus puts fear into Hektor's heart and turns the Trojans in flight toward the city, Patroklos pursues them, despite Achilleus's orders.
He might have broken into the city if the god Apollo, standing on the rampart, hadn't pushed him back, four times. On Patroklos's fourth attempt, the god tells him that he is acting against the decrees of fate – that not even Achilleus will take the city. Patroklos backs off.
Shortly afterward, Hektor immediately comes face to face with Patroklos. Patroklos throws a rock and kills Hektor's chariot driver, Kebriones.
A free-for-all battle erupts over the body of Kebriones.
Soon enough, however, the god Apollo swoops in and strikes Patroklos between the shoulders.
He also knocks the helmet off his head, shatters his spear, detaches his shield, and pries off his breastplate.
Suddenly defenseless, Patroklos is speared in the back by Euphorbos, a Trojan warrior, who then darts away.
Now Hektor comes up to Patroklos and stabs him in the guts – dealing a mortal wound.
With his dying breath, Patroklos tells Hektor, "You were only the third person to kill me. First came Apollo, then Euphorbos. And besides, I can see your death coming."
Then he dies.
Patroklos makes his final appearance near the beginning of Book 23, when his ghost appears to Achilleus in a dream.
(Obviously, there is an ambiguity here: it could just be Achilleus's imagination. Still, we're going to give the dream the benefit of the doubt and say that it could well be the spirit of Patroklos.)
Patroklos asks Achilleus to burn his body quickly. He explains that his spirit can't be accepted into the underworld until his body has been disposed of.
Knowing that Achilleus will die soon, Patroklos requests that their bones and ashes be mingled together in a single urn. That way, they can be together in death just as they grew up together.
Achilleus tries to embrace the ghost, but his hands pass through it. With a shriek, the apparition vanishes.