Accepted for publication in A&AThe Crab nebula was observed with the H.E.S.S. stereoscopic Cherenkov-telescope array between October 2003 and January 2005 for a total of 22.9 hours (after data quality selection). Observations were made with three operational telescopes in late 2003 and with the complete 4 telescope array in January - February 2004 and October 2004 - January 2005. The observations are discussed and used as an example to detail the flux and spectral analysis procedures of H.E.S.S., and to evaluate the systematic uncertainties in H.E.S.S. flux measurements. The flux and spectrum of gamma-rays from the source are calculated on run-by-run and monthly time-scales, and a correction is applied for long-term variations in the detect...