Dr. Samuel Johnson's Preface to Shakespeare (1756) taught critics after him how to do critical analysis of a poet in terms of a) the relationship between literature and nature, b) locating a writer in his own times and judging his merits by comparing him with others of his times, c) how to evaluate a writer's works from the perspective of the critic's own times, and d) finally, the importance of balanced criticism.
The first critical aspect which has to do with literature and human nature was not new. Classical authors such as Homer and Virgil followed this principle: they tried to depict human nature as authentically as possible. What was new in Dr. Johnson's method was his rationality and sense of balance. He did discuss the merits of Shakespeare in terms of the bard's faithful rendition of human nature, but in the second part of the Preface he balanced it with his discussion of Shakespeare as an Elizabethan writer.
The importance of the literature/human nature discussion has to with another, still popular belief about great literature: that it is universal. Dr. Johnson tried to prove Shakespeare's greatness, not through the power of his own opinion, but through logic. Since human nature does not really change through the agaes, he argued, at least in terms of the raw emotions of love, hate, jealousy and such like, writers who are able to authentically describe these emotions stand the test of time. Ordinary writers, Johnson opines, fall away by sticking too close to their times. They are not able to depict human nature well. Shakespeare, by contrast, was able to portray human emotions in such a way that readers reading him after two hundred years could relate to them. It was after Samuel Johnson that this method of establishing universality of literature through the litmus taste of authentically depictiing human nature became a recognized method of criticism.
Johnson was also the first critic to discuss a writer in detail in terms of his life and times. He actually perfected the method in his Lives of the Poets where he showed critics how to use biography to interpret a writer's work. This method of criticism gained huge popularity immediately after Johnson, lasting right through the twentieth century, being challenged only when American New Criticism came into being and critics began to question the wisdom of reading too much into texts, influenced by the writer's biography and the history of the times. But again, it is important to point out that Dr. Johnson's greatness was his ability to balance biographical criticism with universality.
Johnson was also a big advocate for "fairness" in criticism. Literary criticism, he maintained early in the Preface is not a scientific treatise which, when factually accurate, cannot be disputed. But it is precisely because of this, that literary critics have the responsibility to be fair. Thus, he devoted a whole section of the Preface to what he considered Shakespeare's weakness, of which he pointed out three: a) Shakespeare didn't seem to care too much about moral instruction in his plays, b) he wasn't too careful about the historical facts in his history plays, and c), famously, Johnson detested Shakespeare's penchant for punning. Moden critics would now largely disagree with perhaps all three types of Johnson's complaints. But what is important in terms of his contribution to literary criticism is that he encouraged critics to discuss both the good and bad qualities of a writer.