"Odysseus and his crew land on the island in a dense fog.... On the third day, Odysseus and his company of men set out to learn if the Cyclops are friends or foes.(The Odyssey 374)"
"...a drying rack with cheeses, pens crowded with lambs and kids, each in its class.... We lit a fire, burnt an offering, and took some cheese to eat; then sat in silence around the embers, waiting.(Homer 119-135)"
"'You are a ninny, or else you come from the other of nowhere, telling me mind the gods! We cyclopes care not a whistle for your thundering Zeus or all the gods in bliss....'(Homer 176-180)"
Odysseus stays on the island for a few days before going out to the stranger with gifts to see their hospitality and if they would help him and his men out.
"The pike of olive, green though it had been, reddened and glowed as if about to catch. I drew it from the coals and my four fellows gave me a hand, lugging it near the Cyclops... and rammed it deep in his crater eye....while blood ran out....(Homer 286-297)"
Odysseus and his men go into the cave to find cheese and livestock where they wait for the home owner to come back and eat some cheese, filling their stomachs.
"Blinded, and sick with pain from his head wound, the master stroked each ram, then let it pass, but my men riding on the pectoral fleece the giant's blind hands blundering never found.(Homer 351-354)"
Odysseus finds out that the Cyclopes do not care for the Gods and fear for their men whiling taking note of the monsters' views.
"The blind thing in his doubled fury broke a hilltop in his hands and heaved it after us....'Cyclops, if ever mortal man inquire how you were put to shame and blinded, tell him Odysseus, raider of cities, took your eye: Laertes' son, whose home's on Ithaca!'(Homer 395-419)"
All the men prepared a heated and sharpened tree trunk to create a large stake and stabbed the Cyclops' eye, blinding him.
Odysseus tied him and his crew on the underbelly of the sheep and waited till Polyphemus let each ram out to graze, all escaping the death they might have gotten.
Odysseus, with his pride, angered the beast while Polyphemus shot a rock at their ship. He told him his identity and caused a curse upon himself because of it.