He used a codeword, that translates in English rather nicely: "Nobody". He was invisible, and he was taunting Polyphemus the cyclopes with that name and stabbed him on the eye. This made the cyclopes disintegrate and was seen no more.
he gave him wind so the cyclops was drunk
he said his name was nobody so when they attacked the cyclops and the other cyclpopes heard him scream, they asked who was attacking him and the cyclops...
He didn't do anything horrible to him, he ate most of his men, and swore he would eat Odysseus later. But then Odysseus drove a stake into his eye, and escaped by holding onto the undersides of the...