Analyzing how The Importance of Being Earnest gets laughs. If you don’t think the play is funny, just analyze things about it that are trying to be funny. Possible areas to explore: how does the play setup a plot situation with comic possibilities(the concepts of misrepresentation and mistaken identity will probably come up). You may focus on one or two comic moments, or take a more general approach, but the point is to look at the events of the play and the structure of the situation, and discuss how the plot and situations lead to comedy and laughter.
Below is the link of the play which you will need to read.