We present a classical description of the interaction between localized surface plasmon resonances and excitons which can occur in molecular or solid state systems. Our approach consists of adopting a semianalytical description of the surface plasmon resonances in metal nanoparticles and a semiclassical description of the electronic transitions related to the excitonic material. We consider three plasmon-exciton coupling configurations, namely a (or a set of) metal nanoparticle(s) uniformly coated with an excitonic material, a set of metal nanoparticles placed in the vicinity of a sub-wavelength-sized "patch" containing the active material, and the limiting case of a single point dipole coupled to a metal nanoparticle. Our key result is the derivation of the conditions required to achieve strong plasmon-exciton coupling as evidenced by polaritonic splitting. We apply our results to describe recent experimental studies on these hybrid systems. Our study provides a simple, yet rigorous prescription to both analyze and design systems that exhibit strong light-matter interactions as mediated by localized surface plasmon resonances (i.e., particle plasmons).