We describe a first-principles atomistic approach to calculate the electronic and atomic dynamics of nanoscale conductors under steady-state current flow. The approach is based on a self-consistent solution of the Lippmann-Schwinger equation within the density-functional formalism for a sample connected to two bare metallic electrodes with a finite bias. Three-terminal device geometries can also be described easily using the present approach. The formalism provides the most fundamental quantities to describe the dynamics of the whole system: the self-consistent electronic wave functions. With these, the forces on the atoms are determined according to a Helmann-Feynman-like theorem that takes into account the contribution of the continuum of states as well as of the discrete part of the spectrum. Examples of applications will be given in the case of molecular devices with different anchoring groups at the interface between the molecule and the electrodes. In particular, we find that conductances close to the quantum unit (2e(2)/h) can be achieved with a given molecular structure simply by increasing the atomic number of the anchoring group..