Tools of Characterization
Since Giovanni's Room is written in the first person, we're often scouring the text to see if David portrays the events truthfully. Yet, there are certain things that one doesn't question and those are the events themselves.
Regardless of what David says, we learn a lot about him from the fact that he leaves his home in Brooklyn, from the fact that he proposes to Hella, from the fact that when she returns he leaves Giovanni's room without saying a word. The general gist, clearly, is that he has a tendency for taking flight, for doing things without thinking about the emotions of others, for abandoning people.
As for Hella, we learn the most about her from the fact that she leaves for Spain after David proposes, from the fact that she accepts, from the fact that she follows David in Nice and immediately leaves him after learning that he is gay. Like David, she sometimes makes decisions without thinking about them, but she is more prone to snap decisions and is honestly looking for love instead of trying to evade it.
Now let's look at Giovanni: he was married; he left Italy when his child was born dead; he let Guillaume take him under his wing; he seduced David; he killed Guillaume. When one lays out the events of Giovanni's life, it seems that the death of his child is when things turned to tragedy. It is not hard to see how each action after that is simply bringing him a bit closer to disaster.
There is no omniscient third-person narrator in Giovanni's Room. Everything is subjective. Yet characters often try to describe each other, and the descriptions might be seen to open windows on both the describer and the described.
Here's an example. David says,
Giovanni liked to believe that he was hard-headed and that I was not and that he was teaching me the stony facts of life. It was very important for him to feel this: it was because he knew, unwillingly, at the very bottom of his heart, that I helplessly, at the very bottom of mine, resisted him with all my strength. (2.1.52)
If we were not reading closely, we would simply take away that Giovanni is "hard-headed" and likes to tell other people how things are. Yet, at the same time, we realize that David's perception of Giovanni is colored by the fact that he is resisting him. If David were a more open lover, we have no way of knowing if Giovanni would still seem hard-headed and stubborn.
The result is that we get a sense for both David and Giovanni, but the sense is incomplete. It's like the two character descriptions are crippled and leaning on one another.
David has a tendency for judging people by their looks. Like Jacques, he is almost immediately taken in by Giovanni's beauty. By contrast, an unattractive flamboyantly gay man in the bar disgusts him. As he says, "his utter grotesqueness made me uneasy; perhaps in the same way that the sight of monkeys eating their own excrement turns some people's stomachs" (1.2.22). Never mind the fact that he and Giovanni turn out to be very well suited to one another. The point is that Giovanni already had the cards stacked in his favor.
Consider one specific extremely telling physical detail. After Hella discovers that David is gay and resolves to leave him, she appears in the house with her bags packed. David says, "She was extremely cold, she was bitterly handsome" (2.5.101, our italics). It's not that the word "handsome" is inapplicable to women, but in this situation, it's extremely telling. It suggests that David perceives some masculine quality in Hella, which perhaps is what attracted him to her in the first place.
If you look back through the text, you'll find a number of similarly rich physical details, but remember to pay more attention to the observer than to the observed.
Thoughts and Opinions
Giovanni's Room is full of witty banter between the characters. At times, it seems that theirs are just words on the wind, but more often, we get a glimpse into their personalities by the ideas that they casually express.
We'll zoom in on that first conversation between Giovanni and David. When they first speak, they compare Paris and New York. David thinks that in Paris you feel "all the time gone by" (1.2.90). In New York, you feel "all the time to come" (1.2.92). A moment later, Giovanni begins making fun of Americans, and a little rift opens up between them. If we observe the conversation closely, we find that we don't simply learn things like: Giovanni doesn't like America; David thinks that Paris is weighted down by the past.
Instead, we think about all of the indirect ways that they are speaking one another, flirting with one another. For example, David's views on Paris and New York are deeply personal. When he was in New York, he was young and didn't know anything about himself. Yet when he came to Paris, he found that he had the same problems he had in New York, that he couldn't outrun himself by changing locations.
In daily life, we often get to know one another by talking about things other than ourselves, and it is an art that the characters have mastered in Giovanni's Room.