The art of acting entails temporarily living as a different person in a different reality. When you realize this, stepping into your character's skin will become not only easier but also more believable to your audience and fellow players. For an actor, it's the situation that is dominant. In everyday life, you enter situations with the circumstances in mind, not your personality or character. The same goes for becoming a character - you must become that person with all his complexities, thoughts and idiosyncrasies.
Study your character. Understand your character's physical characteristics, as well as emotional and mental state. Know the character's history by understanding the context and the time period of the story. This is how you will realize the character's intentions behind each line. Say your lines with the same thought process you believe your character has.
Communicate your character through his lines and body language. Every line should be rehearsed with the discovered intentions to display who your character truly is. Treat each intention as a positive. If your character is cold, more powerful emotional connections can be made with your audience if you communicate that your character is looking for warmth.
Play to your character's private audience - everyone has a private audience. It could be the parent she disappointed or the teacher who she wants to prove wrong. This private audience is all in the mind and may or may not ever show up in the play itself. Make it up from your own experience if necessary. Drawing on your own related emotions well help you manifest those of your character.
Practice characterizing the other players in the scene. Think of how your character sees and thinks of the other characters. Maybe he sees one as beneath him and the other as loveable or dangerous. Believe those feelings toward the other characters when rehearsing your lines with them. Even if you are quiet, those beliefs will show in your eyes and expressions.