  We investigate the effects of charged impurity distributions and
carrier-carrier interactions on electronic transport in graphene on SiO$_2$ by
employing a self-consistent coupled simulation of carrier transport and
electrodynamics. We show that impurity clusters of characteristic width 40--50
nm generate electron--hole puddles of experimentally observed sizes. In the
conductivity versus carrier density dependence, the residual conductivity and
the linear-region slope are determined by the impurity distribution, and the
measured slope can be used to estimate the impurity density in experiment.
Furthermore, we show that the high-density sublinearity in the conductivity
stems from carrier-carrier interactions.
