The study of silicate melts from first principles is computationally intensive due to the need of relatively large atomic systems and long simulation runs. Recent advances in hardware and software have made it possible to accurately simulate the liquid phase at pressures and temperatures that are geophysically relevant. This paper reports the details of the methodology used in the context of simulations and subsequent analysis of the output data. The simulations are performed using the parallel first-principles molecular dynamics (FPMD) technique within the framework of density functional theory. Various physical properties including the equation of state, thermodynamics, atomic and electronic structures, self-diffusion and viscosity are obtained from simulations. The position time series are visualized to gain insight into underlying physical mechanisms. We review the recent first-principles studies of three liquids along the MgO-SiO2 join including MgSiO3 melt to show that the structural and dynamical properties of these liquids are highly sensitive to pressure and temperature.