The coupled electronic-nuclear dynamics at molecule-metal interfaces are fundamental processes that underlie many distinct areas of science: from electrochemistry, chemisorption, heterogeneous catalysis, quantum dots, all the way to molecular conduction. Simulating these coupled dynamics at molecule-metal interfaces is very challenging, due to the breakdown of the Born-Oppenheimer approximation and the inclusion of a manifold of electrons from the metal. Two methods are presented to investigate these nonadiabatic dynamics: a) In the outer sphere regime (weak electronic coupling between molecule and metal), a surface hopping approach is developed to treat nuclear motion classically with electronic motion captured by hopping between different potential energy surfaces; b) In the inner sphere regime (strong electronic coupling between molecule and metal), electronic dynamics are incorporated into a frictional force (i.e. electronic friction) together with a random force. In addition, a natural combination of these two methods called a broadened classical master equation (BCME) is developed. As benchmarked against numerical exact solutions, the BCME works well in both inner and outer sphere regimes. Finally, a universal form of electronic friction is derived. Such a formula unifies many different forms of electronic friction in the literature and allows the inclusion of electron-electron interactions, and can demonstrate interesting Kondo resonances at low temperature.