Several bacteria and bacteria strands form biofilms in different environmental conditions, e.g. pH, temperature, nutrients, etc. Biofilm growth, therefore, is an extremely robust process. Because of this, while biofilm growth is a complex process affected by several variables, insights into biofilm formation could be obtained studying simple schematic models. In this manuscript, we describe a hybrid molecular dynamics and Monte Carlo model for the simulation of the early stage formation of a biofilm, to explicitly demonstrate that it is possible to account for most of the processes expected to be relevant. The simulations account for the growth and reproduction of the bacteria, for their interaction and motility, for the synthesis of extracellular polymeric substances and Psl trails. We describe the effect of these processes on the early stage formation of biofilms, in two dimensions, and also discuss preliminary three-dimensional results.