Research your character. Figure out his mannerisms, ideas, passions, strengths and weaknesses. Knowing your character thoroughly will help you to portray him more naturally.
Rehearse your part on your own time, and videotape your performance. Watch to see which actions and dialogue seem natural and which ones seem forced or stilted. This exercise will help you to refine your acting toward a more natural presentation.
Gesture only when appropriate. Some actors tend to use too much body language during a scene, which creates an unnatural vibe.
Concentrate on the moment. Your present actions and dialogue are what you need to focus on, rather thinking about what you're going to do or say a minute or several minutes later.
Breathe slowly, and consciously relax your muscles before and during a scene. Muscle tension and anxiety can cause you to seem unnatural.
Think about your own life experience in order to produce authentic emotions. For example, if you are playing a character who has a sad experience, think of your own personal experiences that made you sad.