We use ab initio simulations to investigate the adsorption and the self-assembly processes of tetracyanoquinodimethane (TCNQ), tetrafluoro-tetracyanoquinodimethane (F4-TCNQ), and tetrasodium 1,3,6,8-pyrenetetrasulfonic acid (TPA) on the graphene surface. We find that there are no chemical bonds at the molecule-graphene interface, even at the presence of grain boundaries on the graphene surface. The molecules bond to graphene through van der Waals interactions. In addition to the molecule-graphene interaction, we performed a detailed study of the role played by the (lateral) molecule-molecule interaction in the formation of the, experimentally verified, self-assembled layers of TCNQ and TPA on graphene. Regarding the electronic properties, we calculate the electronic charge transfer from the graphene sheet to the TCNQ and F4-TCNQ molecules, leading to a p-doping of graphene. Meanwhile, such charge transfer is reduced by an order of magnitude for TPA molecules on graphene. In this case, it is not expected a significant doping process upon the formation of self-assembled layer of TPA molecules on the graphene sheet.