We study the phenomenon of anchoring and anchoring transitions in the nematic-substrate system using the Landau-de Gennes formalism. The free-energy functional is expanded around the bulk tensor nematic order parameter up to the second-order terms. This quadratic approximation is used to find an explicit condition for the anchoring direction in a semi-infinite system, and then the phase boundaries between the homeotropic, planar, and conical anchorings are determined. In the cases that we have studied the quadratic approximation predicts a first order homeotropic-conical transition and a first order or continuous planar-conical transition. It also predicts a simple asymptotic expression for the free energy of a finite system, when the sample thickness is large and the deviation of the director from the anchoring direction is small. This asymptotic formnula leads in a natural way to the definition of the geometrical measure of the anchoring strength (b) over bar. However, the quadratic approximation is insufficient to predict the correct behavior of (b) over bar close to a continuous anchoring transition, although it can serve as a rough estimate of (b) over bar far from the transition.