To analyze how an author develops a theme, one needs to look at the literary devices the author used to draw out the theme because it is through these devices that the author also develops the theme. Some literary devices to consider looking for in your analysis are "character development, setting, mood, plot, point of view, figurative language, allegory, symbolism, and irony" ("Identifying Themes and Literary Analysis"). The development of the theme of death should be a fairly easy one to analyze seeing as how the play ends with multiple deaths.
One good way to analyze the development of the theme of death is by looking at character development. If we look closely, we see many of the characters who die share character traits in common that many of the characters who do not die don't share. What the characters who die have in common is a preference to act upon rash, impetuous, violent, passionate emotions rather than rational thought. Tybalt, for example, is the second character to die, and we see in the very first scene that he is quick to judge and has a fiery temper. We see both his quickness to judge and his fiery temper when he quickly assumes that Benvolio is starting a fight with the servants rather than trying to break up the fight. Tybalt's hasty, emotionally driven decision leads to a whole-city riot. Romeo and Juliet are also two characters that make rash, impetuous, emotionally driven decisions, as evidenced by their decisions to marry so suddenly as well as their convictions to commit suicide. In contrast to these characters, Benvolio is the one character who is rational, sensible, and the only peace lover. We see his rational, sensible side both when he tries to persuade Romeo to forget about Rosaline and when he tries to convince Mercutio to get off the street the day that Mercutio is killed, warning that if they should meet any Capulets, "[they] shall not scape a brawl" (III.i.3). We even see his all-important peace loving side in the very first scene when he tries to break up the fight between the servants, saying, "Part, fools! / Put up your swords. You know not what you do" (I.i.59-60).
This contrast between the rational Benvolio who does not die and all of the emotionally driven characters who do die shows us that Shakespeare used character development to develop his theme of death, ultimately making the point that allowing oneself to be governed by irrational emotions rather than rational thought can lead to dire consequences.