The growth mechanisms of epitaxial Si nanowires (NWs) grown by electron beam evaporation (EBE) and catalyzed through gold droplets are identified. NWs are seen to grow both from adsorbed Si atoms diffusing from the substrate and forming a dip around them, and from directly impinging atoms. The growth of a 2D planar layer competing with the axial growth of the NWs is also observed and the experimental parameters determining which of the two processes prevails are identified. NWs with (111), (100) and (110) orientation have been found and the growth rate is observed to have a strong orientation dependence, suggesting a microscopic growth mechanism based on the atomic ordering along (110) ledges onto (111)-oriented terraces. By properly changing the range of experimental conditions we demonstrate how it is possible to favor the axial growth of the NWs, define their length and control their crystallographic orientation.