We report on the nucleation and growth mechanism of self-catalyzed InAs nanowires (NWs) grown on Si (111) substrates by chemical beam epitaxy. Careful choices of the growth parameters lead to In-rich conditions such that the InAs NWs nucleate from an In droplet and grow by the vapor-liquid-solid mechanism while sustaining an In droplet at the tip. As the growth progresses, new NWs continue to nucleate on the Si (111) surface causing a spread in the NW size distribution. The observed behavior in NW nucleation and growth is described within a suitable existing theoretical model allowing us to extract relevant growth parameters. We argue that these results provide useful guidelines to rationally control the growth of self-catalyzed InAs NWs for various applications.