Character is revealed through their actions, obviously.    What your central character (protagonist) does and how he or she does it usually says a lot about them as a person.  The word protagonist comes from the Greek words protos first and agonistes actor.  He or she is the conveyor of your theme.  How your protagonist resolves the conflict by stories end will usually reveal your story's main theme. 

One way to develop character is through the peeling away of the character's layers, showing us more and more of the character's true nature.  As the audience learns more and more about the character, they begin to assimilate whether or not this is a character they like or want to spend any time with.  Okay, movies where there were no redeemable qualities for the main characters. There are not many of those, if any.   You have to have the audience connect with at least one of your characters. Have to have.

The process of revealing these layers is through action, back story, exposition (defined as the necessary information needed to move the story forward) and dialogue.  So in effect you're adding characteristics to your characters as the story evolves.  Lots of professional writers take issue with the term Character Arc.  Because this implies that a character must undergo a significant enough of a change that by story's end it is apparent. The process of characterization does not have to be a process of change, though most stories demand that.  But the process of characterization can be the process of revealing character.

Revealing character is best handled when there can be an action and reaction.  Characters show their true nature best when they are acting.  Something happens and the character responds, often with his own action or in-action.  In "Gladiator", Maximus (Russell Crowe), upon discovering his family?s murder, decides to take no action when forced into Gladiatorial service.  He refuses to fight, scrapes from his skin his Roman Legion markings, and as an audience we understand and immediately connect with this character.  You lose your will to live let alone fight when something like that happens.   So, image if the screenwriters immediately made him into this vengeful assassin.  A kind of "Commando" (the 1980s Arnold Schwarzenegger flick, and an awful one at that) meets "Gladiator", wouldn?t that have been a disaster?  Sure, still an understandable reaction, but that?s not near as effective when trying to establish a truly sympathetic character that the audience will connect.  "Gladiator" is one of the few action/adventure war movies that everyone seemed to enjoy, both men and women.  The themes of family, honor, loyalty struck a cord with everyone in the audience.