How is Odysseus known for his cunning and cleverness?
One must keep in mind that Odysseus, although cunning and clever in many ways, consistently gets assistance from the gods--especially Pallas Athene. However, a good example of his own cunning happens in Book IX when he develops a way to get out of the Cyclop Polyphemus's cave. Odysseus gets the Cyclop drunk on wine. Then, he and his men hang on the bellies of the ewes, which enables them to escape.
Also, Odysseus was cunning in his plan to tie his men to the ship against their will on the island of the Lotus-Eaters. This prevented the men from swimming back to the island only to fall asleep at the hands of their captives and not return to Troy.