Read the play before you go see it. This allows time for the characters and their stories to sink into your mind. This also allows time for you to imagine the world of the play before it's presented to you. Make a few notes about the characters and what the play means to you. Decide whether the play is a morality tale or a cautionary one. Identify the hero of the story, and figure out what makes this character heroic.
Discard preconceptions of the play before you see it. Perhaps you studied "Hamlet" in school years ago, and now you're going to see it of your own volition. Try to forget the movies you've seen of the play, and go in with an open mind. You might see something you never realized was there. Interpretation is a personal process, so don't allow your mind to be affected by preconceptions.
Look for symbols in the play. Images such as flowers, blood, playing cards and swords can signify deeper meanings. In "A Streetcar Named Desire" by Tennessee Williams, the character Blanche hangs a paper lantern over an incandescent bulb because she thinks it's vulgar to leave the bulb uncovered. She says she wants magic, and the lantern provides that for her. This sentiment goes straight to the heart of Blanche, because she has spent her life hiding in a fantasy world. This world is later destroyed. The lantern tells a great deal about Blanche's struggle with her outward self, her past, and her inability to reconcile them.
Look for themes in the play. In "Hamlet," the title character doesn't take action against the man who killed his father until the very end of the play. However, he says to his friend, "The readiness is all." This is a theme of the play. Hamlet is saying that man must always be ready to take action when honor is at stake. In the end, Hamlet doesn't act soon enough and dies, but not before finally killing the man who killed his father. The theme works as a framework through which to see the characters. Other themes are love, fear, friendship, faith and the passage of time. Search for the theme in plays and ask yourself how the characters relate to the theme.
Research the time period in which the play was written. Compare the themes and characters to the social norms of the time. Shakespeare was held to scrutiny that modern playwrights never had to endure. Many plays during his time couldn't make outright political statements, unless they were in favor of Queen Elizabeth. Veiled references in praise of her appear in Shakespeare's plays upon closer scrutiny. Modern playwrights can basically say whatever they like. Understanding the social and artistic restrictions the playwright endured can give you further insight into plays.