In spite of a rapid growth of data processing software, that has allowed for a huge advancement in many fields of chemistry, some research issues still remain problematic. A standard example of a troublesome challenge is the analysis of multi-component mixtures. The classical approach to such a problem consists of separating each component from a sample and performing individual measurements. The advent of computers, however, gave rise to a relatively new domain of data processing – chemometry – focused on decomposing signal recorded for the sample rather than the sample itself. Regrettably, still a very few chemometric methods are practically used in everyday laboratory routines. The Authors believe that a brief ‘user-friendly’ guide-like article on several ‘flagship’ algorithms of chemometrics may, at least partly, stimulate an increased interest in the use of these techniques among researchers specializing in many fields of chemistry. In the paper, five different techniques of factor analysis are used for the analysis of a three-component system of fluorophores. These algorithms, applied on the excitation-emission spectra, recorded for the ‘unknown’ mixture, allowed to unambiguously determine its composition without the need for physical separation of the components. An example of using chemometric methods for physical chemistry research is also provided. For each presented technique of the data analysis, a short description of its theoretical background followed by an example of its practical performance is given. In addition, the Reader is supplemented with a basic information on matrix algebra, detailed experimental ‘recipes’, reference specialist literature and ready-to-use MATLAB codes.