A technique to find the steady-wave solutions in slab waveguides with or without Kerr nonlinearities is presented. This approach is based on the use of space-phase diagrams. It can simplify the resolution and the interpretation of linear problems, as well as provide a way to get the dispersion relation and power dependence of nonlinear waveguides. The technique is applied to a variety of three-layer waveguides exhibiting Kerr nonlinearities. The power dependence of the effective index is computed for all of these waveguides.