I suppose there are many nuances to the revelation of character but for me the two most present in any work of fiction are what a character does and what he/she say and how these things direct his/her emotional and intellectual world.
Sometimes we try to tell how a character is feeling and that is that bad kind of telling that writing craft books are always decrying. (There is a good kind and I wish those books made this distinction and I'm sure some of them do but I've seen many that don't. Good telling--info that doesn't need to be shown...but that's another post). Also authors might think something to the point of exhaustion for both themselves and the reader.
So revelation of characters, in my humble opinion, should be shown through the action they take in the various situations that the story requires them to move through. These will be choices they make and others that are made for them and that they react to.
But for me--I LOVE DIALOGUE Yansky...what characters say to each other can reveal just as much. Each character tells a lot about who they are both in the way they say things and the things they say. Again sometimes they're initiating the conversation, moving it along, and sometimes they're reacting to what others have said.
Also dialogue shows the voices of characters who aren't narrating the story. It not only gives them their say but shows who they are by the way they say what they say.
For me, a lot of how I get my characters comes from how they talk.
Elmore Leonard, in talking about writing dialogue, said that he would let his characters talk and he'd follow the interesting ones. He'd kill off the ones who weren't interesting. Harsh? That's a writer for you.
What characters do and say are most important for me.