The saddle point method is very useful for obtaining asymptotic estimates on the coefficients of an analytic function via the evaluation of contour integrals. Its general approach is to use a contour that crosses a so-called "saddle point", where the modulus of the integrand is maximized, and then locally estimate the integral near this point. I will give a gentle overview of the method, starting with the simpler saddle point bounds, and end with applying the method to several classic combinatorial examples.