A massive foreground cluster lens changes the shapes (shear effect) and number density (magnification effect) of the faint background galaxy population. In this paper we investigate how the shear, magnification and combined information can be used to constrain cluster mass profiles in the weak lensing regime. We develop maximum likelihood techniques to make quantitative predictions for each of the methods. Our analytic results are checked against Monte Carlo simulations. In general, we find that the shear method is superior to the magnification method. However, the magnification information complements the shear information if the former has accurate external calibration. For the magnification method, we discuss the effects of random and systematic uncertainties in the background galaxy counts.