The variational method (Rayleigh-Ritz), Galerkin's method and the method of least squares have been utilized extensively in electromagnetic theory to solve various field problems. In most cases, one makes a formal use of the techniques. In this paper, a tutorial approach has been taken to bring out the mathematical distinctions between the variational method (Rayleigh-Ritz), Galerkin's method and the method of least squares. Examples have been presented to illustrate the strong and weak points of each of the techniques. Finally, the rates of convergence of the three techniques have been derived. It is hoped that with the appearance of this paper, application of a particular technique to solve an electromagnetic field problem would be more rigorous rather than formal.