One of the great qualities of Odysseus in the works of Homer is his cunning. Therefore, there are many places in the the Odyssey, which speaks of his cleverness. So, I will have to be selective.
First, the most obvious case of his cunning is his dealings with Polyphemus, the cyclops. When he is trapped with his men in the cave, he is able to escape through cunning. First, Odysseus gets Polyphemus drunk and then blinds him. He also makes him open the mouth of the cave to escape. In other words, he uses Polyphemus' strength against himself to his advantage.
Second, he is also able to overcome Circe with the use of magic. So, when Circe turned his men into pigs, he was able to take her by surprise and make her restore his men.
Third, he is also a master at disguises and strategy. So, when he finally gets back to his home in Ithaca, he is able not only to lay low, but also create the right time for attack. He does this and is able to kill all the suitors.