What trick does Odysseus devise to get past Cyclops? After, he is blinded, Cyclops sits in the doorway of his cave to catch anyone who tries to escape.
Prior to Odysseus's cunning plan to sneak his men out of Polyphemus's cave by tying them underneath sheep so that the Cyclops cannot feel them, he first needs to blind the Cyclops so that the monster will not be able to see them. Odysseus knows that if he simply kills Polyphemus, he and his men will never be able to move the stone away from the door to the cave and that they will all perish in the cave together. Thus, he knows he must injure the Cyclops in a way that will make it more difficult for the monster to catch them but so he can still move the stone.
When Odysseus left his ship, he'd brought with him a skin of very potent wine given to him by Maron, a priest of Apollo, in Ismarus. He essentially gets Polyphemus drunk on this wine, waits until the monster passes out, and then blinds the Cyclops with a stake he and his men have sharpened and hardened in the fire. Now, the monster will not be able to spot Odysseus and his crew as they are tied under the sheep, and he will only think to feel for the men on top of the sheep (because he's not as cunning as Odysseus is).
Even before he blinds the Cyclops, crafty Odysseus has told the Cyclops that his name is Nobody (or No one, depending on your translation) After Odysseus blinds the Cyclops, he and his men escape by hanging onto the undersides of sheep. As the sheep pass by the Cyclops to go out to graze, the Cyclops runs his hand over the tops of the sheep - to make sure they are sheep and that Odysseus and his men aren't riding out. They escape that way. As the Cyclops calls to his brothers all he can say is that Nobody has hurt me. Odysseus, however, can't seem to be quiet, and after he and his men are safely away from the Cyclops, Odysseus reveal his name to the Cyclops. Not a good idea as the Cyclops is a son of Poseidon (who is already angry with Odysseus).