From the distance on an island, Odysseus and his men see a Cyclops. They decides to go on the island and begin to eat the food that they find there. They then set out to find out whether the Cyclops is a friend or foe.
They go inside a cave and come across Polyphemus. He traps them in the cave using a boulder and eats some of Odysseus men. Now Odysseus has to figure a way out of the cave.
Odysseus comes up with an idea that will get them out of Polyphemus's cave. He offers Polyphemus wine and he falls asleep, Odysseus takes this opportunity to carry out the next step to his plan.
"Odysseus and his crew land on the island in a dense fog and spent days feasting on wine and wild goats and observing the mainland, where the Cyclopes live. On the third day, Odysseus and his company of men set out to learn if the Cyclopes are friends or foes (Collections 6 pg 374)"
While Polyphemus is sleeping, Odysseus and his men make a sharp stick and stab Polyphemus in the eye with it, blinding him. Odysseus and his soldiers decide to hide under sheep and try to make it past Polyphemus.
" Then he dismembered them and made his meal,... if I killed him then we perished there as well, for we could never move his ponderous doorway slab aside. So we were left to groan and wait for morning. (Homer 195-210)"
"'Cyclops, try some wine. Here's liquor to wash down your scraps of men... even as he spoke, he reeled and tumbled backwards, his great head lolling to one side: and sleep took him like any creature (Homer 255-280).'"
Polyphemus notices that his prisoners have escaped. He calls upon his father, Poseidon to curse Odysseus and make his journey back to Ithaca even harder.
"So with our brand we bored that great eye socket while blood ran out around the red hot bar. Eyelid and slash were seared; the pierced ball hissed broiling, and the roots popped (Homer 296-299)."
"Blinded, and sick with pain from his head wound, the master stroked each ram, then let eit pass, but my men riding on the pectoral fleece the giant's blind hands blundering never found (Homer 151-154)"
When Polyphemus opens the rock to let his sheep graze, Odysseus and the others slip out by hiding under the sheep. Polyphemus doesn't notice they leave because they are hiding under the sheep, this is how they escape.
"'Grant that Odysseus, raider of cities, never see his home: Laertes son, I mean who kept his hall on Ithaca. Should destiny intend that he shall see his roof again among his family in his father's land, far be that day the dark years between. Let him lose all companions and return under strange sail to Bitter days at home (Homer 445-452)."