The method I would suggest would be to create individual sections to focus on to organise your study, for example, genre, character, costume, plot, theme and staging. This will help you identify the type of play you are analysing, make connections between plot and character developments, analyse character motivations, recognise recurring motifs and themes, pick out dramatic devices at work and how they are used to impact the audience. In addition, it is important to understand the difference between a playtext and a piece of literature, like a novel. A play is meant to be staged, and so, take note of the staging choices, the lighting and sound techniques, stage directions, costumes and set. One way of doing this is imagining how you would stage the scenes, dress the characters and direct the actors. You could also watch previous performances and different adaptations of the play you are studying to compare various director choices and discuss why they made these decisions.
In addition, to ensure a greater understanding of the play you should research the context, for instance, what was the cultural, societal and political climate at the time it was written, who would be the audience at the time it was staged, who was the playwright, what was the playwright’s intentions, how did critics review the play. This will help you analyse and question how the context is evident and influences the play. Moreover, reading other critic’s writings on the play will help you form your own argument and analysis.