Massive black holes (MBHs), in contrast to stellar mass black holes, are expected to substantially change their properties over their lifetime. MBH masses increase by several orders of magnitude over a Hubble time, as illustrated by Sołtan's argument. MBH spins also must evolve through the series of accretion and mergers events that increase the masses of MBHs. We present a simple model that traces the joint evolution of MBH masses and spins across cosmic time. Our model includes MBH-MBH mergers, merger-driven gas accretion, stochastic fueling of MBHs through molecular cloud capture, and a basic implementation of accretion of recycled gas. This approach aims at improving the modeling of low-redshift MBHs and active galactic nuclei (AGNs), whose properties can be more easily estimated observationally. Despite the simplicity of the model, it does a good job capturing the global evolution of the MBH population from z ~ 6 to today. Under our assumptions, we find that the typical spin and radiative efficiency of MBHs decrease with cosmic time because of the increased incidence of stochastic processes in gas-rich galaxies and MBH-MBH mergers in gas-poor galaxies. At z = 0, the spin distribution in gas-poor galaxies peaks at spins 0.4-0.8 and is not strongly mass dependent. MBHs in gas-rich galaxies have a more complex evolution, with low-mass MBHs at low redshift having low spins and spins increasing at larger masses and redshifts. We also find that at z > 1 MBH spins are on average the highest in high luminosity AGNs, while at lower redshifts these differences disappear.