We may sometimes infer indirectly from the spectrum that two stars are present because of the presence of spectral lines from both a cool star and a hot star. Since these are unlikely to be produced in a single star, this suggests that the light is actually the light of two stars. A more direct way to infer the presence of a binary system uses the Doppler effect, as illustrated below.
Because of the motion around the center of mass, spectral lines are periodically blue shifted and then red shifted for each star. This is illustrated schematically for a single line coming from each star.