The Ising model is studied by the generating functional approach in order to provide a better understanding of that method. It is shown how to derive a general solution of a functional equation in terms of infinite-dimensional integrals. This solution is not unique; the different possibilities are characterized by different paths of integration. Further, the saddle point approximation is used for the integrals in order to obtain second-order correlation functions. It is shown that besides the normalsolution, one obtains several anomalous ones, which correspond directly to the nonphysical solutions of the transfer matrix method for treating the partition function. It is also shown that only the correct solution can give a realistic behavior of the correlation function at large distances. The relevance of the saddle point methods for describing phase transitions is also discussed.