A new methodology is given to determine basic parameters of flares from their X-ray light curves. Algorithms are developed from the analysis of small X-ray flares occurring during the deep solar minimum of 2009, between Solar Cycles 23 and 24, observed by the Polish Solar Photometer in X-rays (SphinX) on the Complex Orbital Observations Near-Earth of Activity of the Sun-Photon (CORONAS- Photon) spacecraft. One is a semi-automatic flare detection procedure that gives start, peak, and end times for single ("elementary") flare events under the assumption that the light curve is a simple convolution of a Gaussian and exponential decay functions. More complex flares with multiple peaks can generally be described by a sum of such elementary flares. Flare time profiles in the two energy ranges of SphinX (1.16 - 1.51 keV, 1.51 - 15 keV) are used to derive temperature and emission measure as a function of time during each flare. The result is a comprehensive catalogue - the SphinX Flare Catalogue - which contains 1600 flares or flare-like events and is made available for general use. The methods described here can be applied to observations made by Geosynchronous Operational Environmental Satellites (GOES), the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and other broad-band spectrometers.