Tools of Characterization
Characterization in American Beauty
Family Life
Right off the bat, we can tell that the Burnhams are dysfunctional because of the way they interact with each other. In their first interaction, it's clear Carolyn has no respect for Lester, as she asks him sarcastically if he could make her any later as he heads out to the car in the morning.
Then, when his suitcase pops open and his papers spill everywhere, his daughter offers only a "Nice going, Dad." Oh, and this is all after Carolyn criticized Jane's outfit by asking her if she was actively trying to be unattractive.
From just these few seconds of footage and dialogue, we see that Carolyn is a pretty intense taskmaster who expects a lot of her family (and is often disappointed), Lester's family views him as pathetic, and Jane feels alienated from both of her parents since she's a disappointment to her mother and her father is a disappointment to her. The family dynamics speak volumes before we've even really had a chance to dig into the story.
Actions
Of course, nothing really says more about a person than what they're wiling to do.
For example, we can tell that Lester is pretty mixed up inside when he decides to overhaul his whole life over an attraction to a teenaged girl. Sure, he needed to shake things up, but the fact that his "reinvention" comes with a lot of juvenile behavior suggests that he's not really the most mature guy.
On the flip side, we can tell that he's grown a lot at the end of the film when he stops short of sleeping with Angela, having realized that she's way, way too young for him. After that decision, he really seems to be at peace with his life and himself—that is, he's calmed the heck down and is finding satisfaction in more mundane things. He dies smiling at a photograph of his family, rather than while driving his new car or having sex with Angela… and that says a lot about how far he's come.
Clothes
In a couple of places, the movie draws attention to what characters are wearing and what that says about them. Carolyn criticizes Jane for dressing purposely (in her view) unattractive. There's really nothing particularly wrong with Jane's outfit, but she definitely isn't trying to stand out or be noticed, which speaks to some level of insecurity on her part.
Carolyn is also insecure, of course, but she battles it by trying to make sure that everything around her is immaculate—and that includes what she's wearing. As Lester points out in one of his early voiceovers, even her gardening clogs match her clippers—that's how serious she is about image.
Speech and Dialogue
The dialogue gives us quite a few clues to what's going on inside the minds of the characters—although it can be misleading.
Angela is a good example of this misdirection: she goes on and on (and on) to Jane about how attractive she is to men and how much sex she's had, which makes her seem pretty conceited.
But late in the film, she tells Lester that she's actually a virgin, which means that, presumably, all that blabbing about being promiscuous was really just a cover for insecurity. So, in this case, the way she talks about herself gives us a false impression at first, but eventually it reveals how insecure and vulnerable she really is.