Spectral analysis is the main tool of astrophysical research. Current instrumental technology offers very sensitive CCD detectors with enough spectral resolution for many purposes. This introductory text is aimed at graduate students starting a thesis in X-ray astronomy, and at non-specialists who wish to analyse X-ray data themselves. It gives the basic tools and explains the basic issues often implicit in specialised papers. X-ray spectroscopy differs from spectroscopy at longer wavelengths because it is photon based with relatively small numbers of photons. As a result the Poisson process is at the core of the statistical description of X-ray spectra. The classical model-fitting procedure is described and illustrated on a detailed example. It is applicable to any parametric model and any instrumental data. High resolution X-ray spectroscopy, now applicable to many sources thanks to sensitive grating instruments, allows to measure individual lines accurately. The diagnostics that it offers are very similar to those offered by mid-resolution optical spectroscopy: line ratios, line broadening, absorption lines.