There is a strategy for how to write an essay on a play. Writing about a theater production is not difficult if you know how to break the production down to its key parts. You do not need to cover every aspect of the production when writing about it, but choose the elements that frame a coherent story for your essay and expand on those elements accordingly.
Read the original script and consider the themes of the play. Analyze any edits made from the original script's transition to the stage version and make note of any how any omitted scenes effect the final outcome. Consider the effects that certain dialogue edits may have on character development. Also take into consideration the motives for any edits to the original script and view them through the lens of the director to gain an insight into the story that this particular production is presenting.
Consider the directing and acting and how it effects your interpretation of the original script. Compare the play to other productions of it that you have seen or to film adaptations to add to your perspective. If this is your first time seeing this script performed, then consider how the actors interpreted the script and how that adds or detracts from a character's traits that you perceived when you read the script. Consider the blocking, or stage movement, of the actors and how it works with the story, as well. Note any special talents such as singing or dancing and how they act as a vehicle for the talent and contribute to the overall experience of the play.
Analyze the director's overall interpretation of the original script. Directors sometimes put a spin on a play to make it more relevant to a particular audience.
Critique the set design, costumes and makeup. Look for the props and how they help set the story in a certain time or place. Do the same for the costumes, as well, particularly if you are analyzing a period piece. Think about the costumes and their relation to the play. In a well-done production, everything is done for a reason and every piece contributes to the story. Is that the case with the play you are writing about? Consider that and view the production through this lens.
Note the lighting and sound of the play. Are all of the lights up during the entirety of the production? This could be done due to a lack of technical aptitude or for artistic reasons, and is worth your consideration. Notice how the lighting effects the play and also note any special effects. For instance, if a smoke machine is used for fog, does the technician running this moderate the machine so as to not detract from the overall production?
It is not uncommon for a director to stage a production of classic plays such as "Othello" set in a modern setting such as a high school. If this is done consider how it effects the emotional content of the script and how well the director executed his vision in the different setting.