What quotes show that Odysseus uses what he has learned in order to reach his goal?
I would say that in the course of the epic Odysseus learns that there is a right time to reveal who he is. If we untangle Homer's chronology, we see that after Odysseus leaves Troy (see Book 9), one of his first critical encounters results in him revealing his true identity to the Cyclops:
“Cyclops, if any man asks how you came by your blindness, say that Odysseus, sacker of cities, Laertes' son, a native of Ithaca, maimed you.” (A.S. Kline translation)
This revelation causes Odysseus great difficulty after this point because Polyphemus is able to identify Odysseus to his father Poseidon, who then assails Odysseus while he is on the open seas.
Thus, when Odysseus returns to Ithaca, he is very careful not to reveal who he is until the right moment. He keeps his identity from Athena in Book 13; he conceals his identity from the swineherd Eumaeus until just the right moment. He makes sure that his old servant Eurycleia remains quiet after she discovers his identity in Odyssey 19:
but now a god has inspired you and you have found me out be quiet and keep it from all the rest of the house. (A.S. Kline translation)
And, of course, Odysseus does not reveal his identity to the suitors until he has collected enough evidence against them to justify slaughtering them:
‘The guest in your hall has not disgraced you. I have not missed the target, nor did it take me long to string the bow. My strength is undiminished, not lessened as the Suitors’ taunts implied. Well now it is time for the Achaeans to eat, while there is light, and afterwards we shall have different entertainment, with song and lyre, fitting for a celebration.’ (A.S. Kline translation)
Odysseus even hides his identity from his wife and father until he believes that the time is right.
In sum, I would say the key to Odysseus' success is knowing when to reveal his true identity to people.