How does Odysseus display hubris?

Hubris is having too much pride and believing you can do no wrong. It is self-confidence run amok.
Odysseus has many reasons to be proud of himself, especially in the context of his warrior culture. He is strong, brave, wily, smart, and overall a good leader. But he brings disaster his way when he gets too cocky.
The most famous example of his hubris is when, having blinded the Cyclops and made his escape, he can't resist shouting out his identity to his injured foe. This allows the god Poseidon to punish him and his crew:

if any man on the face of the earth should ask who blinded you, shamed you so – say Odysseus, raider of cities, he gouged out your eye…

This is a extremely foolish thing to do. The smart move would have to been to get away unidentified, but Odysseus cannot stand the idea that the Cyclops wouldn't know who had bested him. Odysseus just has to have credit for what he did, as if there will be no consequences. It is like having to tell your enemy that you robbed his bank.
And then, still swaggering, Odysseus has the nerve—or hubris—to say to his men:

Did I not keep my nerve, use my wits, to find a way out for us.

Odysseus will learn to be less arrogant, but not yet.

An additional example of Odysseus's hubris comes in Book IX when he tears into his men, calling them "mutinous fools." They are indeed in a restless mood. After all, the men are starving, and so they don't take kindly to Odysseus telling them to put to sea after they've barely finished plundering Ismara— the land of the Cicones.
In recounting his tale, Odysseus puts the blame squarely on his crew's shoulders for the misfortunes that subsequently befall them, such as an attack by Ciconian reinforcements. In blaming his men for everything that's gone wrong, Odysseus is displaying great pride and arrogance, not to mention a distinct lack of leadership. He can't very well blame hungry, thirsty men for wanting to take the opportunity to fill their bellies. That he does so is a clear indication of hubris.

Another important Greek idea is hubris. In our modern usage of the word, it means excessive ego or pride. In ancient Greece, it meant specifically excessive pride toward the gods. Many tragedies occur because a human defies or insults a god. In The Odyssey, Odysseus’s hubris gets the better of him when he taunts Polyphemus. He is so confident and arrogant about his triumph over the Cyclops that he makes a terrible mistake. When he gives his real name to Polyphemus, he incites the anger of Polyphemus’s father, the sea god Poseidon.