Density functional theory seeks to solve for an approximate form of the electronic density of a system.  In general, atoms are split into ionic cores and valence electrons.  The ionic cores (nuclei plus non-bonding electrons) are assumed to be stable and are treated as a single object.  Each valence electron is treated separately.  Thus, for example, a Lithium atom is treated as two bodies – Li+ and e- – while oxygen is treated as three bodies, namely O and 2e.
The “true” ground state of a crystal system is generally unsolvable.  However, the variational theorem assures us that any guess as to the electronic state function of a system will overestimate the ground state energy.  Thus, by beginning with a suitably parametrized guess and minimizing the energy with respect to each of those parameters, an extremely accurate prediction may be made.  The question as to what one's initial guess should be is a topic of active research.
In the large majority of crystal systems, electronic relaxation times are orders of magnitude shorter than ionic relaxation times.  Thus, an iterative scheme is adopted.  First, the ions are considered fixed and the electronic state is relaxed by considering the ionic and electron-electron pair potentials.  Next, the electronic states are considered fixed and the ions are allowed to move under the influence of the electronic and ion-ion pair potentials.  When the decrease in energy between two iterative steps is sufficiently small, the structure of the crystal is considered solved.