In Book 22, Odysseus finally reveals himself to the suitors who have plagued his homeland and his household. He does this by killing Antinous with an arrow through the throat in an extremely graphic and bloody way. The suitors don't immediately realize who he is, until he announces himself and their impending doom. He begins to fight, after refusing to accept a weak apology from Eurymachus, and dispatches Eurymachus as quickly as he did Antinous, with an arrow through the chest. The remaining suitors begin to arm themselves, with help from Melanthious (a servant whose loyalties now belong with the suitors).
Athena shows up, once again disguised as Mentor, and Odysseus calls out to her, requesting her aid:
“Mentor, help fight off disaster. Remember me, your dear comrade. I’ve done good things for you. You’re my companion, someone my own age.” (22, 262-266)
The suitors follow up Odysseus' request for aid by threatening Mentor (Athena) with death if he fights with Odysseus. This angers the goddess, but she is still resolved to test Odysseus instead of making sure that he wins the fight outright.
The fight begins in earnest and Athena makes sure that when all of the suitors throw their spears they miss Odysseus, but Telemachus is grazed on the wrist. (22, 325-327) Eventually, after she's convinced of Odysseus' worthiness, Athena demonstrates her godhood by flashing her sigil/shield in the air to highlight her backing of Odysseus. This also causes the suitors to flee. (22, 374)
Essentially, Odysseus does the majority of the work, but Athena helps him out by keeping the spears from hitting him.