Electronic noise has its roots in the fundamental physical interactions between matter and charged particles, carrying information about the phenomena that occur at the microscopic level. Therefore, Low-Frequency Noise Measurements (LFNM) are a well-established technique for the characterization of electron devices and materials and, compared to other techniques, they offer the advantage of being non-destructive and of providing a more detailed view of what happens in the matter during the manifestation of physical or chemical phenomena. For this reason, LFNM acquire particular importance in the modern technological era in which the introduction of new advanced materials requires in-depth and thorough characterization of the conduction phenomena. LFNM also find application in the field of sensors, as they allow to obtain more selective sensing systems even starting from conventional sensors. Performing meaningful noise measurements, however, requires that the background noise introduced by the measurement chain be much smaller than the noise to be detected and the instrumentation available on the market does not always meet the specifications required for reaching the ultimate sensitivity. Researchers willing to perform LFNM must often resort to the design of dedicated instrumentation in their own laboratories, but their cultural background does not necessarily include the ability to design, build, and test dedicated low noise instrumentation. In this review, we have tried to provide as much theoretical and practical guidelines as possible, so that even researchers with a limited background in electronic engineering can find useful information in developing or customizing low noise instrumentation.