Theme
Just as in a short story or poem, the author of a play is examining a theme or set of themes. And, as with a short story or poem, a play may be interpreted in different ways by different readers.
The themes of a play can be suggested in many ways.
First, look at the title of the play. Some titles give you quite broad hints as to theme: Proof and Almost, Maine, for example.
The characters of a play often represent larger ideas, as do all of the characters in Almost, Maine, for example.
The conflicts between the characters can suggest themes, as the clash between Catherine and Claire introduces the question of the relationship between insanity and genius.
Conflicts between characters and society or nature can also provide insight to themes. In Hamlet, for example, Ophelia wants to marry Hamlet; her father warns her away from him, because princes don't have the freedom to marry for love; their marriages are arranged for political expediency. This introduces the issue of whether marriage should be based on romantic love or on practical considerations.
Lines or exchanges of dialogue can also give clues to theme. In Proof, the arguments between Catherine and Hal all raise the issue of trust: in our dealings with the outside world, we must demand proof, but in our personal relationships, is it better to trust, or to ask for proof?
Look for hints about theme in the staging: the setting, the lighting, the music, and the props. In Almost, Maine, for example, the sets and props are simple, to reflect the bare-bones lives the people have, and also to emphasize the action and interaction on the stage: this play is about relationships, not money, and any props are meant to symbolize that: the heart in the bag, for example, or the tattoo on Jimmy's arm.
When you read a play, as when you read a short story or poem, read with an open, receptive mind. Usually, a play has more than one theme, and usually it asks more questions than it answers. Thus, many interpretations of theme can be correct, as long as they can be supported with evidence from the play.