The process of second-harmonic generation (SHG) in a finite one-dimensional nonlinear medium is analyzed in parallel by the Green-function technique and the Fourier-transform method. Considering the fundamental pump field propagating along a given direction and eliminating back-reflections at the boundaries the terms giving the surface second-harmonic fields in the particular solution of the wave equation are uniquely identified. Using these terms the flow of energy corresponding to the surface second-harmonic fields is analyzed in the vicinity of the boundaries. The formula giving the depth of the nonlinear medium contributing to the surface SHG is obtained. Both approaches for describing the SHG are compared considering complexity and quantization of the interacting fields. In addition, a theoretical model of surface SHG in centrosymmetric media is proposed. The model is built upon assumption that the second-order nonlinearity decays exponentially with distance from the boundary. As an important example, the generation of surface SHG from a thin dielectric nonlinear layer placed on a silicon substrate is analyzed by the proposed model.