The method of kinetically controlled selective ionization (KCSI) for investigating collisional energy transfer in highly vibrationally excited molecules is presented in detail. In this first paper of a series the focus is on the key concepts and the technical realization of KCSI experiments to provide a common basis for following reports on our available results of KCSI studies on the vibrational relaxation of a variety of larger molecules. The KCSI technique directly monitors the energetic position and shape of the population distributions g(E,t) during the relaxation process by means of an energy selective two photon ionization process via an electronic intermediate state. Such measurements allow-for the first time-to extract complete and accurate experimental sets of transition probability distributions P(E＇,E) even at quasicontinuous densities of states. Basic energy transfer quantities are already obtained from a straightforward analysis of the arrival time and width of the KCSI curves. A master equation formalism is outlined which is the basis of a data inversion providing a complete evaluation of the experimental information content. Various examples of characteristic KCSI data on collisional deactivation of highly vibrationally excited molecular populations are used to discuss important aspects of the quality and the general character of P(E-＇,E) parameters deduced from such measurements. The conditions for a successful modeling of these data are very tightly bound, and the resulting energy transfer parameters are therefore of high precision. In Paper II [J. Chem. Phys. 112, 4090 (2000), following article] we give a full account of the toluene KCSI experiments. We will deal with our completed studies on azulene, azulene-d(8), pyrazine and pyridine in follow-up publications of this series. (C) 2000 American Institute of Physics. [S0021-9606(00)01504-X].