To be believable an actor needs to truly study their character. There is a very simple method that an actor can use to do this. It is called the GOTE method. GOTE is a very easy to remember acronym. It stands for Goal, Obstacle, Tactics and Expectation. This is a very basic approach to breaking down a character. Now lets go over each of these objectives.
Goal is what the character is going after. It is the whole purpose for the play. The goal kicks off all of the action. The goal is to be persuaded by the character. Now the goal can't be general, it needs to be something very specific. For example a general goal would be "I want to feel fulfilled by marrying someone." A more specific goal would be "I want John to marry me." The goal needs to be very targeted. A good exercise is to imagine you are starving and there is a sandwich just out of your reach. Now try to reach for it. That is how you need to be when going after your goals.
The obstacle is what stands in the way of the goal. The obstacle needs to be in direct opposition to the goal. For example if the goal is "I want John to marry me" the obstacle may be "My parents hate John." The character needs to struggle with the obstacle to reach their goal. This is what makes a play interesting and not just 2 people having a conversation about the weather on stage.
Tactics are what a character uses to overcome the obstacles and reach the goal. This is were a play gets fun. The tactics make the character real. The tactics a character chooses shows the audience what type of person they are. The tactics can be funny, honorable, deceitful, etc. There can be multiple tactics used by an actor. A good actor will be able to move from tactic to tactic with ease in order to achieve the goal.
Expectation gives tone and excitement to the tactics. This is what stops the goals from being too academic and boring. It shows what is the characters excitement and enthusiasm behind their goal.
You can find what the character's GOTE is by just studying the play. An actor should take notes when reading a play. You can set up a GOTE sheet to have with you as you read. Just take a paper and write Goal, Obstacle, Tactics and Expectation. It is also helpful to write name, sex, age, marital status, education and make up a typical day in the life of the character (a day that does not take place during the play).
It really doesn't take that much extra work to setup a GOTE sheet. A character needs to come alive to the viewer. They need to draw the viewer into their world. An actor needs to do everything to create a character and world that is 100% believable. Studying a character's GOTE sheet can add the 3rd dimension to a character that is often missing in theater.