What were the tricks (ruses) used by both Odysseus and Penelope in Part 2 of The Odyssey by Homer?
One way in which Odysseus tricks the suitors in Homer's The Odyssey is to return to his home dressed as a beggar. The suitors are foolish enough to believe that a beggar is not worthy of their concern and several suitors throw footstools at him. They dismiss Odysseus because of his appearance and attire. It is unwise to "judge a book by its cover."
Book 17 describes Odysseus' appearance as he enters him home in disguise:
...Odysseus came inside, looking like a poor miserable old beggar, leaning on his staff and with his clothes all in rags.
Antinous is rude and disdainful toward Odysseus, but he is not the only suitor who treats Odysseus poorly. By his interactions with each man, Odysseus is able (on the advice of Athene) to see what kind of person each man is. Odysseus has placed himself in the hall and no one fears him. It will be that much easier for him to punish the suitors when the time comes.
It has been noted that Penelope tricks the suitors by unraveling at night the weaving done by day on the shroud she says she is weaving for Odysseus. She has promised to choose a husband from the suitors when the shroud is finished. She succeeds in this ruse for three years before her trickery is exposed.
Penelope's final trick (in Book 23) is designed to make sure Odysseus is who he says he is, and not a god pretending to be her husband. To test his story, she orders Euryclea to move his bed back into his room. (She knows this is impossible, for Odysseus built the room around a tree from which his bed was carved.)
Euryclea, take his bed outside the bed chamber that he himself built. Bring the bed outside this room, and put bedding upon it with fleeces, good coverlets, and blankets.
When Odysseus hears this, he becomes angry believing someone has moved the bed:
Who has been taking my bed from the place in which I left it? He must have found it a hard task, no matter how skilled a workman he was, unless some god came and helped him to shift it. There is no man living, however strong and in his prime, who could move it from its place...
When Penelope hears this, she finally believes that Odysseus has returned to her. Penelope is presented as a clever woman who does a fine job of outsmarting the suitors for a very long time, and is even able to trick the wily Odysseus into proving what he says to be the truth.