First, the Sparknotes summary:
The scene changes abruptly. Hermes leads the souls of the suitors, crying like bats, into Hades. Agamemnon and Achilles argue over who had the better death. Agamemnon describes Achilles’ funeral in detail. They see the suitors coming in and ask how so many noble young men met their end. The suitor Amphimedon, whom Agamemnon knew in life, gives a brief account of their ruin, pinning most of the blame on Penelope and her indecision. Agamemnon contrasts the constancy of Penelope with the treachery of Clytemnestra.
Back in Ithaca, Odysseus travels to Laertes’ farm. He sends his servants into the house so that he can be alone with his father in the gardens. Odysseus finds that Laertes has aged prematurely out of grief for his son and wife. He doesn’t recognize Odysseus, and Odysseus doesn’t immediately reveal himself, pretending instead that he is someone who once knew and befriended Odysseus. But when Laertes begins to cry at the memory of Odysseus, Odysseus throws his arms around Laertes and kisses him. He proves his identity with the scar and with his memories of the fruit trees that Laertes gave him when he was a little boy. He tells Laertes how he has avenged himself upon the suitors.
Laertes and Odysseus have lunch together. Dolius, the father of Melanthius and Melantho, joins them. While they eat, the goddess Rumor flies through the city spreading the news of the massacre at the palace. The parents of the suitors hold an assembly at which they assess how to respond. Halitherses, the elder prophet, argues that the suitors merely got what they deserved for their wickedness, but Eupithes, Antinous’s father, encourages the parents to seek revenge on Odysseus. Their small army tracks Odysseus to Laertes’ house, but Athena, disguised again as Mentor, decides to put a stop to the violence. Antinous’s father is the only one killed, felled by one of Laertes’ spears. Athena makes the Ithacans forget the massacre of their children and recognize Odysseus as king. Peace is thus restored.
This Book has the feel of being an interpolation, a coda added to the epic by later hands in order to round it off - though many scholars would argue that the epic as a whole is the work of many hands, so it may not make sense to speak of "interpolations".
We start with another glimpse into the underworld - the "Little Nekyia", so called to distinguish it from Odysseus' longer encounter with the dead in Book 11. The scenes in the underworld don't quite tie in with those in Book 11. Akhilleus, for one, is portrayed quite differently, and his extended conversation with the deceased Agamemnon undercuts the pathos of his shorter and bleaker appearance in the earlier Book.
When he hears about Odysseus' successful return, Agamemnon praises Penelope's fidelity. He reminds us (once again) that his own homecoming was followed shortly afterwards by his death at the hands of his own wife, the faithless Klytaimnestra. This passage contains a prediction of the Odyssey itself, when Agamemnon declares that Penelope will have kleos (fame) in song in future years. In fact, Homer's celebration of Penelope extends some way beyond the stereotypical feminine virtue of fidelity.
We find Odysseus emotionally reunited with Laertes, though not before Odysseus has tricked his father by pretending to be someone else. Laertes asks him to identify himself by saying where he is from and who his parents are - the last time that this characteristic formula appears in the epic. The Book ends with a depiction of Laertes, Odysseus and Telemakhos - a triad of the male masters of the household, now all reunited at last. Among the last lines are these, from Laertes:
What day is this for me, dear gods? Indeed I rejoice:
my son and my grandson are competing in excellence.