We propose a docking method that mimics the way proteins bind. The method accounts for the dominant driving forces at the different length scales of the protein binding process, allowing for an efficient selection of a downhill path on the evolving receptor-ligand-free energy landscape. Starting from encounter complexes with as much as 10 A rms deviation from the native conformation, the method locally samples the six dimensional space of rigid-body receptor-ligand structures subject to a van der Waals constraint. The sampling is initially biased only by the desolvation and electrostatic components of the free energy, which capture the partial affinity of unbound structures that are more than 4 A away from the native state. Below this threshold, improved discrimination is attained by adding an increasing fraction of the van der Waals energy to the force field. The method, with no free parameters, was tested in eight different sets of independently crystallized receptor-ligand structures consistently predicting bound conformations with the lowest free energies and appropriate stability gap around 2 A from the native complex. This multistage approach is consistent with the underlying kinetics and internal structure of the free energy funnel to the bound state. Implications for the nature of the protein binding pathways are also discussed.