Unit cell parameters (a,b,c,α,β,γ) can be computed from the final relaxed positions of the ions.  In a NaCl calculation, the final position of the Na ion might be (0,0,0) in picometer Cartesian coordinates and the final position of the Cl ion might be (282,282,282).  From this, we see that the lattice constant would be 584 pm.  For non-orthorhombic systems, the determination of cell parameters might be more complicated, but many ab-initio numerical packages have utilities to make this calculation simpler.
Once the lattice cell parameters are known, patterns for single crystal or powder diffraction can be readily predicted via Bragg's Law.