I believe that the first thing Odysseus did to outwit the cyclops was giving the cyclops some very strong wine. It is said that the cyclops never had wine before, so he was intrigued by the drink. The cyclops drank the wine, and became extremely drunk...The cyclops thanked Odysseus for the wine, and asked for his name. Odysseus told the cyclops that his name was "No man." The Cyclops then suddenly collapsed into a drunken sleep. While the cyclops slumbered, Odysseus and his men took some timber that they had sharpened into a spear, and heated the sharpened end in the fire. Once the spear was almost glowing red, they pushed it into the cyclops eye. The confused cyclops immediately woke up, and screamed out of pain. Now, the cyclops was completely bind. Some of the other cyclops who lived near by, ran to Polyphemus's (the cyclops) side, asking how this happened, who had done this horrible thing to him. The cyclops said, “No man!” and the other Cyclops all returned home laughing...Early the next morning, Odysseus tied each of his men to the belly of one of the giant sheep that belonged to the cyclops. When the cyclops finally awoke, he led the sheep out of the cave. The cyclops made sure to feel the back of each sheep to make sure no one was on them. Though, feeling nothing, Polyphemus allowed each sheep to pass out of the cave, which resulted in carrying Odysseus and his men out of the cave.
I hope this helped!