The structural characterization of polycyclic aromatic hydrocarbon molecules adsorbed on graphene is of fundamental importance in view of the use of graphene or graphene nanoribbons for electronic applications. Before reaching this point, one has to determine the structure of the adsorbed molecules. Here, we study the case of benzene, coronene, and hexabenzocoronene on a graphene layer. First, the adsorption properties of single molecules are calculated using first-principles calculations at the level of density functional theory. We benefit from a recent scheme, particularly adapted for weakly adsorbed molecules, allowing us to precisely calculate the van der Waals contribution. Then, scanning tunneling microscopy (STM) is used to produce images of self-assembled molecules comparing different theoretical approaches to experimental observations. Finally, we consider the imaging of isolated molecules, and we show how the STM tip influences the molecule position by soft mechanical interaction during the scanning process.