The operator product expansion seems to be a quite useful tool. In an attempt to find a full concise complete computation, involving deriving the coefficients, and introducing the taxonomy associated with using this tool, I have hit a wall. The gentle starting point of A(x)B(y) =sum C * (new Operator) is usually stated and the rest assumed to be common knowledge. If we consider the case of a simple free field (composite field), how does one find the coefficients and what is this new operator and what is its physical significance. I think I tend to fair well when things are laid out fully and explicitly, not abstractly. I think may be the definition and example with energy momentum tensors shown in most conformal field theory textbooks is not what I am looking for. I am looking for hopefully an explicit very simple free quantum field theory showing fully how this is done.