Among all galactic microlensing events, those involving a passage of the observed source star over the caustic created by a binary lens are particularly useful in providing information about stellar atmospheres, the dynamics of stellar populations in our own and neighbouring galaxies, and the statistical properties of stellar and substellar binaries. This paper presents a comprehensive guide for modelling and interpreting the light curves obtained in events involving fold-caustic passages. A new general, consistent and optimal choice of parameters provides a deep understanding of the involved features, avoids numerical difficulties and minimizes correlations between model parameters. While the photometric data of a microlensing event around a caustic passage itself do not provide constraints on the characteristics of the underlying binary lens and do not allow predictions of the behaviour of other regions of the light curve, vital constraints can be obtained in an efficient way if these are combined with a few simple characteristics of data outside the caustic passages. A corresponding algorithm containing some improvements over an earlier approach, which takes into account multisite observations, is presented and discussed in detail together with the arising parameter constraints, paying special attention to the role of source and background fluxes.