At the center of Locke's essays is his commitment to logic and reason, and his rejection of convenient, frilly ideas that seem to him to be clearly unfounded. For instance, when he approaches the question of nature vs nurture, a sensitive philosophical argument during his time, he does so with authority, claiming the philosophy that has since been called, "Tabula Rasa." That's a pretty good place to start an analysis of Locke.
By asserting that man has no preternatural ideas or beliefs, Locke is rejecting a religious or superstitious view of the self as a transcendental entity. New research in the fields on neurology and psychology suggest that in a way, Locke was absolutely correct, but they might add that the human is born with innate abilities to draw conclusions and learn from their environment. Locke's idea of the blank slate is regarded as one of the great claims of Western philosophy.
In order for readers to analyze An Essay correctly, it's important to talk also about the nature of knowledge itself, or epistemology. Locke argues that the way people often conceived of knowledge was begging the question, because to say that someone 'knows' something, they must make an ontological claim for the objectivity of that knowledge, which Locke argues is simply prejudice.
In a few words, Locke's arguments could be summed up like this: It's easy to form beliefs about existence and reality, but just remember that all of them are founded on unprovable assumptions about the nature of knowledge and the nature of reality. We're making the best of our unknowably complex, unexplainable reality.