On the ship, what does Athena tell Odysseus he is to do, and why?
When Athena reveals herself to Odysseus on the shores of Ithaca, she states that she admires him, even though he can be so deceptive. She believes he is the wisest counselor and speaker among men, just as she is the most subtle and diplomatic of the gods; therefore, she will continue to help him, as she has secretly been doing.
She gives Odysseus instructions to hide his treasure (which she influenced the Phaeacians to give him) in a cave, and she explains about the troubles caused by the suitors in his house. He is to tell no one that he has returned, not even Penelope. Until the time is right, he is to "'Bear everything, and put up with every man’s insolence, without a word.’" She explains to him how the suitors have tried for three years to win over Penelope, and how she has remained true to Odysseus in her heart. Athena instructs Odysseus to go stay with his loyal swineherd, Eumaeus, while he investigates all that is going on, and she tells him that she will now go retrieve Telemachus from the home of Menelaus, so that he may join his father. Before she leaves, Athena disguises Odysseus as a pathetic old beggar that no one will recognize him.
Athena doesn't actually explain what Odysseus is to do until he lands on Ithaca. Once there, and he knows who she is, she tells him that he is to remain a secret from his old friends/wife until he has a plan set to kill the suitors. She also tells him that he needs to go to Eumaeus and he will be of help to him. This is where she disguises him as an old beggar.