Odysseus' leadership abilities lie largely in his ability to convince a crowd to follow him. When Helen married Menelaus, Odysseus was the one who convinced the other kings to unite in defense of the marriage. This may have been a hard proposition to sell as the other kings also wanted beautiful Helen's hand in marriage, but with his leadership skills, Odysseus was able to convince them easily.
During the Battle of Troy, Odysseus showcased his leadership skills when he convinced the others to give him Achilles' battle armor and move forward with the Trojan Horse idea. Although the power of persuasion was one of his strongest skills, he displayed additional leadership skills when he took the 10-year journey back to his homeland.
Persistence marked Odysseus' journey along with his clear-headed determination that he would reach home, regardless of how many Cyclops, sorcerers or sirens were between him and his destination. Through each of the scenarios that befell him, Odysseus repeatedly displayed fine leadership skills.
Rather than allowing his men to be eaten by the Cyclops or turned permanently into animals by Circe, he rescued them every time. Sadly, in spite of his efforts, his team died after eating the forbidden cattle of the sun god. However, he eventually got home, where he displayed yet another leadership skill, the desire to lead and the willingness to fight for it.