For Legolas in The Hobbit films, see here. See here for Legolas's family history, and here for his friendship with Aragorn, and here for his friendship with Gimli. For clarification on how the eight functions work, see here.
Dominant Fi: Legolas has a strong internal moral code. He does not care if there will be consequences, he will defend his loved ones and morals no matter what.
Auxiliary Ne: Legolas is very imaginative, exploratory, and abstract (over half of his lines and actions in the books).
Tertiary Si: Legolas starts out holding onto his family's past experiences with dwarves and it takes a personal experience to change his mind (Gimli's deep love for Galadriel).
Inferior Te: Legolas is capable of coming up with basic logical options for action.