Odysseus shows his intelligence several times throughout Homer's epic poems, such as when he helped the Greeks sneak into Trojans camp via the Trojan Horse. The Trojans took this giant wooden horse as a peace offering. When the Trojans were in a drunken stupor, the Greeks came out of the horse and killed the Trojans, thus winning the battle of the Trojan War.
Another example of Odysseus's intelligence was when he outsmarted Polyphemus by telling the cyclops his name was "Nobody." He also had the plan to carve a giant stake out of a tree in order to blind the cyclops, thus enabling him and his men to be freed from Polyphemus's cave via being tied to the underbelly of the cyclops's sheep.
When it came time for Odysseus and his men to cross paths with the Sirens, Odysseus devised a plan to save everyone. He laid beeswax over his men's ears so they were unable to hear the sweet song of the Sirens. Meanwhile, Odysseus had his men tie him to a mast on the ship as to not allow Odysseus to die due to the Sirens' song.
After reaching Ithaca after having been gone for 20 years, Odysseus, with Athena's help, disguises himself as an old man. This meant that the suitors who wanted to marry Odysseus's wife Penelope did not know Odysseus was home. He ended up defeating all of these men, convincing Penelope that he was really Odysseus and earning his pre-war life back.