The method of point-splitting regularization is applied on the two-dimensional (super)conformal field theory. This method is first used to regularize the fermionic conformal field theory and then the N=1 superconformal field theory. We obtain the correct central extensions for the conformal algebra and the N=1 superconformal algebra. We arrived at these results only after some nontrivial, but exact, cancelations among all the singular terms, as required by the consistency of the point-splitting method. In the course of our analysis, we rederive Wick's Theorem directly from the commutation equations of the fundamental fields.