Computational simulation of nonadiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons, to name a few. We report an implementation of the fewest-switches surface-hopping algorithm in the NWChem computational chemistry program. The surface-hopping method is combined with linear-response time-dependent density functional theory calculations of adiabatic excited-state potential energy surfaces. To treat quantum transitions between arbitrary electronic Born-Oppenheimer states, we have implemented both numerical and analytical differentiation schemes for derivative nonadiabatic couplings. A numerical approach for the time-derivative nonadiabatic couplings together with an analytical method for calculating nonadiabatic coupling vectors is an efficient combination for surface-hopping approaches. Additionally, electronic decoherence schemes and a state reassigned unavoided crossings algorithm are implemented to improve the accuracy of the simulated dynamics and to handle trivial unavoided crossings. We apply our code to study the ultrafast decay of photoexcited benzene, including a detailed analysis of the potential energy surface, population decay timescales, and vibrational coordinates coupled to the excitation dynamics. We also study the photoinduced dynamics in trans-distyrylbenzene. This study provides a baseline for future implementations of higher-level frameworks for simulating nonadiabatic molecular dynamics in NWChem.