Independent electron surface hopping (IESH) is a computational algorithm for simulating the mixed quantum-classical molecular dynamics of adsorbate atoms and molecules interacting with metal surfaces. It is capable of modeling the nonadiabatic effects of electron-hole pair excitations on molecular dynamics. Here, we present a transparent, reliable, and efficient implementation of IESH, demonstrating its ability to predict scattering and desorption probabilities across a variety of systems, ranging from model Hamiltonians to full dimensional atomistic systems. We further show how the algorithm can be modified to account for the application of an external bias potential, comparing its accuracy to results obtained using the hierarchical quantum master equation. Our results show that IESH is a practical method for modeling coupled electron-nuclear dynamics at metal surfaces, especially for highly energetic scattering events.