Odysseus's "trick" to getting out of the cave is to blind the Cyclops, Polyphemus, so that the monster can still move the heavy stone away from in front of the door but has a more difficult time trying to locate and catch the men.  Odysseus realizes that if he simply kills the Cyclops, he and his men will also perish inside the cave because there is no way they'll be able to move that stone.  So, he gets Polyphemus very drunk and tells the monster that his name is "Nobody" (another pretty clever trick) and when he passes out, Odysseus and a handful of his crew plunge a large olive stake that they've sharpened and hardened in a fire into the monster's one eye.  Then, when the monster begins to scream and the other Cyclopes come to his aid, he shouts out that "Nobody is hurting [him]" and so they leave.  Then Odysseus and his men lash themselves to the undersides of sheep that they've tied together (another good trick!) so that when Polyphemus feels the animals' backs to be sure that the men aren't riding out on them, he cannot feel them because they are underneath the sheep.

How Does Odysseus trick the Cyclops to get past him in the cave?

Odysseus and his men cut down a tree and sharpened it into an enormous spike, which they hid in the cave. When the Cyclops returned to the cave, Odysseus gave him wine and got him drunk. Before he fell asleep, the Cyclops asked Odysseus his name. The sly Odysseus told the Cyclops, "My name is Nobody."

Once the Cyclops was sound asleep, the men heated the point of the giant spike in the fire then plunged it into the Cyclops's eye. Polyphemus (the Cyclops) ripped the spike from his eye and screamed for help from his brothers. When they asked him who was bothering him, he yelled "Nobody is!" The other Cyclopes ignored him, thinking he was just making fun.

Meanwhile, Odysseus and his men tied themselves to the bellies of Polyphemus's sheep. When the Cyclops pushed the boulder away to try to catch the men as they ran outside, he felt only the woolly sheep, allowing the men to escape. 

What are some of the ways that Odysseus tricks Polyphemus?

The two major ways that Odysseus tricks Polyphemus are by lying about his name and by having his men hide under the sheep.

Odysseus tells Polyphemus that his name is "No Man."  Then when he has put Polyphemus's eye out with the stake, this makes it so Polyphemus cannot get help.  His friends, the other cyclopes, ask him if someone is hurting him and he tells them that "no man" is and they go away.

Then, Odyssesus's men hide under the bellies of the sheep so that they can get out of the cyclopes's cave without him detecting.