We present an atlas composed of more than 1500 spectra of late-type stars (spectral types from G to M) observed simultaneously in the optical and calcium triplet spectral ranges. These spectra were obtained as part of a survey to search for cool supergiants in the Magellanic Clouds and were taken over four epochs. We provide the spectral and luminosity classification for each spectrum (71% are supergiants, 13% are giants or luminous giants, 4% are carbon or S stars, and the remaining 12% are foreground stars of lesser luminosities). We also provide a detailed guide for the spectral classification of luminous late-type stars, the result of the extensive classification work done for the atlas. Although this guide is based on classical criteria, we have put them together and re-elaborated them for modern CCD-spectra as these criteria were scattered among many different works and mainly conceived for use with photographic plate spectra. The result is a systematic, well-tested process for identifying and classifying luminous late-type stars, illustrated with CCD spectra of standard stars and the classifications of our own catalogue.