Perhaps one of the best ways to analyze Johnson's Preface to Shakespeare (1765) is to trace Johnson's arguments that Shakespeare's plays stand "the test of time." Johnson, who was an Aristotelian by nature, believed Aristotle's arguments in the Poetics that literature (in Aristotle's case, plays) can only be successful and universally understood if it mirrored life. Aristotle used the Greek word mimesis to describe a play's ability to imitate life, arguing that literature reflect real life and not the world of fantasy. Johnson agreed.
In the Preface, for example, Johnson noted that Shakespeare's characters
. . . act and speak by . . . those general passions and principles by which all minds are agitated, and the whole system of life is continued in motion. (p. 62)
The argument here is that Shakespeare's characters and their actions mirror the life of men; in fact, in another section of the Preface, Johnson observes that Shakespeare's characters are men rather than heroes, and they appeal to readers of all ages precisely because readers identify with these characters' humanity.
This discussion leads to a more specific way to analyze the Preface--to focus on Johnson's comments about Shakespeare's characterization. If we take the Preface in its entirety, we see that Johnson discusses Shakespeare's plots, language, structure, but more than anything else, Johnson reserves the mass of his comments for how Shakespeare creates characters and their interactions to reflect the universal human experience:
His persons act and speak by the influence of those general passions and principles by which all minds are agitated.
Johnson would argue that readers of all times are able to see themselves in Shakespeare's characters simply because we recognize those "passions and principles" in ourselves.
An analysis of Johnson's views on Shakespeare's articulation of character is a useful way to understand the Preface as a whole.