With Athena's help, Odysseus is able to return to his palace unrecognized and gauge the loyalty of his suitors. While mingling among them as a beggar, he becomes aware of the fact that the "leaders" of the suitors are the least loyal and this makes him angry; he wants to slay them on the spot. However, this tactic would not prove successful. Through constant encouragement from Athena and support from the loyal swineherd, goatherd, and his son, Odysseus is able to hold his tongue until the time to speak is appropriate.
This occurs in Book XXII: "The Battle in the Hall." After the suitors decide to put the bow away for the day and try to bend it again tomorrow, Odysseus reveals his true identity:"Now Odysseus stript off his rags, and leapt upon the great doorstone, holding the bow and the quiver full of arrows," (lines 1-2).
His success in taking the suitors by surprise is immense, especially in their realization that he meant to kill Antinous and didn't do so accidentally. "Poor fools, they did not realize that the cords of death were made fast about them all." (Book XXII, lines 31-33).
The speech he delivers (lines 34-40) is meant to inform the suitors exactly of his motives and to warn them of their impending doom:
"Dogs! you thought I would never come back from Troy, so you have been carving up my substance, forcing the women to lie with you, courting my wife before I was dead, not fearing the gods who rule the broad heavens, nor the execration of man which follows you for ever. And now the cords of death are made fast about you all!"
Since Antinous (leader of the suitors) is already dead, Eurymachus speaks up in an effort to pacify Odysseus and save his own life by blaming the dead man. He agrees with Odysseus that was he's said is "just and right," but insists the man to blame for these misdeeds is already dead, "But there lies the guilty man, Antinous, who is answerable for everything. He was the ringleader..." (lines 45-47). However, in doing so, he only succeeds in speeding the progression of Odysseus's revenge. "Now the choice lies before you, fight or flight, if you wish to save your lives; but I do not think any one of you will escape sudden death," (lines 62-63).
Odysseus's words are prolific, as he succeeds in avenging their misdeeds and securing ownership of his palace once again.