This paper presents a novel, systematic approach to the construction of feedback control for stabilization to a set point of drift-free systems. The method relies on the introduction of a set of guiding functions whose sum vanishes only at the reference set point. The guiding functions are not Lyapunov functions; however, a comparison of their values allows us to determine a desired direction of system motion and permits us to construct a sequence of controls such that the sum of the guiding functions decreases in an average sense. The individual guiding functions are hence not restricted to decrease monotonically but their oscillations are limited and coordinates in a way to guarantee convergence. The method is applied to control a model of a front-wheel drive vehicle. In this case, the choice of the guiding functions is straightforward and gives additional, geometric insight into the steering problem. The guiding function approach presented is general and can be employed to control a variety of mechanical systems with velocity constraints.