We present a general procedure and the associated computational tool for the kinematical description and characterization of nuclear reactions with several fragments in the exit channel. For such processes the emphasis is placed on the purely experimental extraction of the most physically relevant magnitudes and their distributions, which can eventually be compared with the results of generic model calculations. The general capabilities of the approach are illustrated through the results of the application to selected examples, for which various aspects related to inclusive and exclusive measurements are discussed. For the particular case of sequential emission or non-capture breakup we analyze the general problem involved in the determination of intrinsic angular distributions in the rest frame of the decaying nucleus and the design of a specific experiment for a full and uniform coverage of the whole solid angle.