The Epic of Gilgamesh doesn't spend a lot of time getting into characters' thoughts, motivations, and so on. Not that those things aren't important (after all, the whole last three tablets of the epic are about Gilgamesh's quest for knowledge), but you sort of have to figure them out from what you can see. And what you can see are the characters' actions.
Thus, when Gilgamesh laments day and night over Enkidu's body, you can get a powerful sense of how much that friendship meant to him. When he goes to the ends of the earth and beyond in search of an answer to the question about death, you can see how much his fear of mortality is eating at him.
And sometimes, the way a character acts can even reveal something that they might be pretending isn't there. For example, when Ishtar tries to get Gilgamesh to marry her, it would probably be fair to say that she's trying not to appear angry and spiteful—as Gilgamesh accuses her of being. But when Ishtar reacts to Gilgamesh's rejection by sending the Bull of Heaven down to earth to kill him, we start to think Gilgamesh has a point.
With direct characterization, the narrator straight-up tells you what a character is like. In this poem, most of the direct characterization comes near the beginning; once the story picks up, we can see for ourselves what characters are like through their actions and the other things on this list.
Still, it's a big help in Tablet 1 when we get a direct report on how Gilgamesh is an irresponsible tyrant, or how Enkidu is an uncivilized wild man. These remarks by the narrator help set the stage in our minds, which we can fill in later with details we learn along the way.
Our first report on Gilgamesh is that he is "lordly in appearance" (1. 28) and that his body was modeled by Aruru to be "beautiful, handsomest of men, perfect" (1. 49-50). That description, though, isn't just about his outward appearance. We realize pretty quickly that even if he doesn't have a heart of gold, he is the strongest of men and the most powerful too. According to the opening lines, we also know that he has "knowledge of all" (1. 3). So, this is a situation in which judging a book by its cover produces an accurate verdict.
When we first meet Enkidu, he is a wild man, untouched by civilization. So, obviously, he's mostly naked: Enkidu has no covering other some ragged animal-skins (at line 1.90 the poem calls them "a garment like Sumukan," the god of wild animals). Once he meets Shamhat, she—in the grand tradition of women—get him cleaned up: she cuts his hair, wraps him in a cloak, buys him some nice flat front khakis from J.Crew. Voila: Enkidu is now a human.
Or how about when Gilgamesh shows up at Siduri's place? She's terrified of him because he looks like a hot mess—but that judgment makes him rather cranky, and he kind of acts like a wild man by trying to beat her door down. So, at least in Gilgamesh's eyes, his appearance is perfectly reasonable considering where he is coming from—and that tells us that the physical appearance of a character is a window into the emotions and thoughts of a character.
From our discussion about how physical appearance is used, you can probably guess where we're going with this "Location" deal. That's right: because Gilgamesh lives in the city of Uruk at the beginning of the story, we know that he is civilized. Because Enkidu lives in the wilderness, we know that he is a wild man.
Of course, these two characters aren't the only ones who get identified by their location. For example, we know that Utanapishtim and his wife are a pretty special pair, given that they live in an enchanted part of the underworld, beyond the rising of the sun. Sometimes, however, a character's location can be just plain weird. Why does Siduri keep a tavern in the underworld? Who are her customers? We honestly have no idea.
Sex and Love
At the beginning of the poem, Gilgamesh is terrorizing the citizens of Uruk. Part of this involves him forcing the young men of the city to take part in endless athletic contests. But it also involves him forcing the young women of the city to have sex with him. This can tell us several things about Gilgamesh's personality. For one thing, the fact that he is forcing these women into sex against their will shows that he is addicted to power, and doesn't care about the feelings of other people. (Even granting that things like "consent" were probably treated differently 5000 years ago.)
Plus, the fact that no amount of sex seems to satisfy him—he keeps moving relentlessly from woman to woman—shows that there is an underlying absence in his life. Can it be a coincidence that, once Enkidu shows up, we don't hear about him having sex with anyone else? In fact, we actually see him reject sex, with a goddess, Ishtar—the goddess of love, no less! Hmmmm….