The term epistemology comes from the Greek word epist�m�, their term for knowledge. In simple terms, epistemology is the philosophy of knowledge or of how we come to know.
Methodology is also concerned with how we come to know, but is much more practical in nature. Methodology is focused on the specific ways — the methods — that we can use to try to understand our world better. Epistemology and methodology are intimately related: the former involves the philosophy of how we come to know the world and the latter involves the practice.
In its broadest sense, positivism is a rejection of metaphysics (I leave it you to look up that term if you ‘re not familiar with it). It is a position that holds that the goal of knowledge is simply to describe the phenomena that we experience. The purpose of science is simply to stick to what we can observe and measure. Knowledge of anything beyond that, a positivist would hold, is impossible. When I think of positivism (and the related philosophy of logical positivism) I think of the behaviorists in mid – 20 psychology. These were the mythical ‘rat runners’ who believed that psychology could only study what could be directly observed and measured. Since we can ‘t directly observe emotions, thoughts, etc. (although we may be able to measure some of the physical and physiological accompaniments), these were not legitimate topics for a scientific psychology. B.F. Skinner argued that psychology needed to concentrate only on the positive and negative reinforcers of behavior in order to predict how people will behave — everything else in between (like what the person is thinking) is irrelevant because it can ‘t be measured.