This is an interesting question because it asks how the author accomplishes characterization rather than just asking who Jack is. I like it. In Lord of the Flies, William Golding reveals Jack's character through both direct and indirect characterization.
Direct characterization is what Golding tells us directly about Jack. For example, Golding tells us Jack has red hair and is wearing an elaborate choir robe when we first meet him. Most physical description an author uses is considered direct characterization, but it can also include statements about Jack's character.
In this novel, Golding relies more heavily on indirect characterization to reveal Jack's character. Indirect characterization uses the character's own actions and words and their effects on others to reveal character. Readers have to take what they hear Jack say and do, along with how other characters react to him, and make their own judgments about him.
For example, when we first meet Jack, he says:
“I ought to be chief,” said Jack with simple arrogance, “because I’m chapter chorister and head boy. I can sing C sharp.”
When Jack taunts Piggy and calls him names, we understand more about Jack's character. Golding uses Jack's own words to reveal his haughtiness, but he also uses other people's reactions to him to reveal Jack's character. When the boys hold an election, no one votes for Jack at first, not even the choir; however, finally, "with dreary obedience the choir raised their hands." This simple act reveals quite a lot about Jack's character without saying it explicitly. The people who have already experienced his leadership do not want any more if it, but they are also too intimidated by him to vote for the other guy (Ralph).
Golding also uses Jack's actions to indirectly reveal his character. When the three boys go exploring, we surmise that Jack does not appreciate beauty, like Simon, because when he sees the candle buds he slashes at one with his knife. We also infer that Jack does not like to look weak; for example, when he is not quite able to kill a pig the first time he sees one, he is at first embarrassed and then he turns aggressive:
He snatched his knife out of the sheath and slammed it into a tree trunk. Next time there would be no mercy. He looked round ﬁercely, daring them to contradict.
Most of the time, however, Golding uses a combination of direct and indirect characterization to tell the readers about Jack (as well as the other characters). In this passage, Golding combines these techniques:
He looked in astonishment, no longer at himself but at an awesome stranger. He spilt the water and leapt to his feet, laughing excitedly. Beside the pool his sinewy body held up a mask that drew their eyes and appalled them. He began to dance and his laughter became a bloodthirsty snarling. He capered toward Bill, and the mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness. The face of red and white and black swung through the air and jigged toward Bill. Bill started up laughing; then suddenly he fell silent and blundered away through the bushes.
We see Jack's actions, but we also see Bill's dramatic response ands hear Golding tell us that Jack loses all "shame and self-consciousness" when he wears the mask. Readers must use both the character's actions (indirect characterization) and the author's revelations (direct characterization) to make their own judgments about Jack's character.