Density functional theory (DFT) within the local density approximation (LDA) is used to understand the electronic properties of Na1/3CoO2 and Na1/3CoO2(H2O)4/3, which was recently found to be superconducting1. Comparing the LDA charge density of CoO2 and the Na doped phases indicates that doping does not simply add electrons to the t2g states. In fact, the electron added in the t2g state is dressed by hole density in the eg state and electron density in the oxygen states via rehybridization. In order to fully understand this phenomenon, a simple extension of the Hubbard Hamiltonian is proposed and solved using the dynamical mean-field theory (DMFT). This simple model confirms that the rehybridization is driven by a competition between the on-site coulomb interaction and the hybridization. In addition, we find that the presence of eg-oxygen hybridization effectively screens the low energy excitations. To address the role that water plays in creating the superconducting state, we compare the LDA band structure of Na1/3CoO2 and its hydrated counterpart. This demonstrates that hydration does cause the electronic structure to become more two-dimensional.