What does Odysseus learn from his adventures that helps him once he reaches Ithaca?
I would say that the major element Odysseus learns in the course of his adventures that helps him when he returns to Ithaca is patience. Odysseus gets himself into trouble in Odyssey 9, when he reveals his true identity to the Cyclops after blinding him. This revelation leads to Poseidon, who is the father of the Cyclops, attempting to destroy Odysseus upon the seas.
Once Odysseus gets back to Ithaca, he has to wait for the right time and endure a number of insults in his own home before he can make his move to destroy the suitors.
And with that [Antinous] grasped the stool and threw it, striking Odysseus on his back, under the right shoulder. But Odysseus stood firm as a rock, and did not reel at the blow. He merely shook his head in silence, thinking dark thoughts in the depths of his mind. (A.S. Kline translation)
Odysseus has many opportunities to reveal his identity to friends and loved ones in the course of Odyssey 13-21, but until the time is right he allows himself to be known only to his son Telemachus (Odyssey 16) and his aged nurse Eurycleia (Odyssey 19). Just before he springs his trap upon the suitors, he reveals himself to his loyal cowherd Philoetius and the swineherd Eumaeus (Odyssey 21).
Thus, in my estimation, Odysseus' adventures teach him to earn the label that Homer so frequently applies to his hero. He is a "much-enduring" man.