How do Odysseus and his men actually escape from the Cyclop's cave?

Hey stab the cyclops in the eye when he is asleep. Then, when the cyclops is letting his sheep out to graze, Odysseus and his men hid under the sheep as they outside. The cyclops, being blind, had to use his hands and sense of touch to make sure the men didn't escape. Feeling only sheep, the men got away handily.