Define the character's emotional state. Before you can act in an emotional scene, you must first be clear about your character's emotions. Read your lines thoroughly to gain a full understanding, and keep an eye out for dual emotions. For example, your character might be expressing grief with a dramatic show of anger, or may be feigning love when he actually feels revulsion.
Understand your motivations. Study the rest of the script to understand why your character is experiencing the emotional scene. Which events led up to that moment? What other characters are in the scene, and how does your character relate and react to them? How are they involved in the emotional scene? If possible, develop a knowledge of the events that preceded the play; if they are not available, make up details that sound plausible. The more you understand your character's story, the better able you will be to act the role.
Collect similar experiences. Although it may be painful in the case of sad or angry emotional scenes, it is crucial that you be able to experience the same emotions as your character. The more genuine the feeling, the better your performance will be. Think through your past to gather experiences that elicit the emotion your character is showing. Choose events that produce a strong, easily identifiable emotion. If you do not have any, consider events in the lives of people close to you, or make them up.
Call up emotion on cue. Once you have collected your emotional experiences, spend time reliving them. Do it over and over, and be very aware of the physical experience of the emotion. How does your body feel? Does your heartbeat speed up? Do you get tears in your eyes? Hone this physical response until you are able to think of your collection of experiences (or just one) and call up that response on cue.
Apply what you have learned to your scene. With that knowledge, try some classical conditioning with your lines. When you say a line that is supposed to be accompanied by tears, be able to call up that physical and emotional response. Do it over and over until that line is solidly associated with your target emotion. The process should be second nature. Make the experience your character's, so that when you are saying the lines, you are experiencing the emotion as the character.