A step-by-step theoretical protocol based on density functional theory (DFT) and time-dependent DFT at both the molecular and periodic levels is proposed for the design of dye-sensitized solar cell (DSSC) devices including dyes and electrolyte additives. This computational tool is tested with a fused polycyclic pyridinium derivative as a novel dye prototype. First, the UV-vis spectrum of this dye alone is computed, and then the electronic structure of the system with the dye adsorbed on an oxide semiconductor surface is evaluated. The influence of the electrolyte part of the DSSC is investigated by explicitly taking into account the electrolyte molecules co-adsorbed with the dye on the surface. We find that tert-butylpyridine (TBP) reduces the electron injection by a factor of 2, while lithium ion increases this injection by a factor of 2.4. Our stepwise protocol is successfully validated by experimental measurements, which establish that TBP divides the electronic injection by 1.6 whereas Li(+) multiplies this injection by 1.8. This procedure should be useful for molecular engineering in the field of DSSCs, not only as a complement to experimental approaches but also for improving them in terms of time and resource consumption.