In modern life, to make measurements comparable, stating the quality of a measurement in terms of the measurement uncertainty is an absolute necessity. The ISO/BIPM “Guide to the Expression of Uncertainty in Measurement”—usually referred to as the GUM or the Guide—, which was published in 1993, introduces a method to unify the evaluation and the statement of measurement uncertainties. This method has been accepted by almost all calibration services all over the world and has become a quasi-standard in the field of metrology. This paper deals with the background of the GUM, the knowledge of the respective measurement and other fundamental aspects which have been included in the EA-4/02 requirements document published by the European co-operation for Accreditation. It shows how the basic concepts may be converted in a straight forward procedure to evaluate the uncertainty in a measurement. It is an expanded version of a lecture with the same title, held by the author at the workshop “GUM uncertainty budget in calorimetry—questions and ways to realistic determinations of measurement uncertainty” at the 14th Ulm-Freiberg Kalorimetrietage in Freiberg (Saxony) March 21/23, 2001.