"We lit a fire, burnt an offering, and took some cheese to eat; then sat in silence around the embers, waiting...In the glare he saw us (Homer 133-155)."
"...in one stride he clutched at my companions and caught two in his hands like squirming puppies to beat their brains out, spattering the floor. Then he dismembered them and made his meal...(Homer 192-195)."
"'Cyclops, try some wine. Here's liquor to wash down your scraps of men...' (Homer 226-227)."
Odysseus and his men arrived at the island of the Cyclops and found a cave. They decided to stay for a bit to eat and drink. However soon after their small snack break, a giant one-eyed monster walked in, Polyphemus.
"I drew it from the coals and m four fellows gave me a hand, lugging it near the Cyclops...straight forward they sprinted, lifted it, and rammed it deep in his crater eye... (Homer 288-292)."
Without any hesitation, Polyphemus picked up a few of Odysseus's men and ate them like they were a couple of chips. The Cyclops had no hospitality whatsoever.
"I tied them silently together twining cords of willow from the ogre's bed; then slung a man under each middle one to ride there safely... (Homer 337-340)."
Odysseus knows that this wine is very strong and that no one can resist it. By giving it to the Cyclops, he will begin to feel woozy and sleepy. Once he falls asleep, Odysseus can continue his plan.
".'..tell him Odysseus, raider of cities, took your eye: Laertes' son, whose home's on Ithaca!' (Homer 417-419)"
Once the Cyclops is asleep, the team heated up a large wooden spike and shoved it into his eye. The juice of his eye sizzled, until he was blind.
At this point, the Cyclops really wants to catch them, however it will be hard to since he is now blind. Odysseus uses his problem solving skills to tie each man under three sheep so that the Cyclops wouldn't be able to find them as they escaped out the cave.
After they have escaped, Odysseus felt very accomplished and proud that he took Polyphemus's eye. Because of this, he screams out to him as they were leaving that his name was Odysseus. This only makes it worse for them because Polyphemus now can pray to Poseidon to curse Odysseus.