Tools of Characterization
Where would Raskolnikov be without his overcoat? It's not just any overcoat, but a "student's" overcoat (thereby characterizing him as a student). It's also an extremely ragged coat (which characterizes him as an ex-student and poor). He actually has two overcoats. The narrator says he only has the summer one, but then he wraps up in the winter one to go to sleep. But maybe it really is only one overcoat, with two different personalities.
Pyotr Petrovitch Luzhin also is a fun one for this category. Check out what he's wearing when he meets Raskolnikov: an "exquisite pair of lavender gloves"; "Light and youthful colours"; "a cravat of the lightest cambric with pink stripes on it." This outer layer of pastel is meant to make him look young and carefree so girls like Dounia will look at him and guys like Andrey Semyonovitch will let him join their circles. Once we see inside his head, though, we picture him wearing severe, grim colors. Luzhin's clothing categorizes him as a sneak, always hiding something, always disguising his true motives, which can't help but show through.
This one is pretty obvious. We can't analyze Raskolnikov's character without considering his acts of murder. People can't talk about Sonia without bringing up the prostitution. Svidrigaïlov is characterized by his crimes against women and children and by his act of suicide. Razumihin is characterized by his stability, his reliability. He always shows up. We aren't sure about Andrey Semyonovitch until he defends Sonia against Luzhin. Though dreamy and cerebral, this novel is very action-driven. We gain at least a surface understanding of the characters by comparing and contrasting their various actions.
Thoughts and Opinions
When we finally hear Luzhin's thoughts, we realize that he really is a jerk. Hearing a character's thoughts gives us evidence by which to measure their stated opinions. Andrey Semyonovitch is a good example of this. From what Marmeladov told Raskolnikov, we have the impression that he's a bad guy. But, once inside his head, we are pretty sure he didn't beat Katerina or take advantage of Sonia. We've heard lots of bad things about Svidrigaïlov. We know he's not too nice, but some of those things are horrible. And when he tells Raskolnikov he doesn't even think those things were wrong, we know he's probably done even worse than what we've heard.