The Pierre Auger Observatory is designed to study cosmic rays of the highest energies ($>10^{19}$ eV). The ground array of the Observatory will consist of 1600 water Cherenkov detectors deployed over 3000 km^2. The remoteness and large number of detectors require a robust, automatic self-calibration procedure. It relies on the measurement of the average charge collected by a photomultiplier tube from the Cherenkov light produced by a vertical and central through-going muon determined to 5 - 10% at the detector via a novel rate-based technique and to 3% precision through analysis of histograms of the charge distribution. The parameters needed for the calibration are measured every minute, allowing for an accurate determination of the signals recorded from extensive air showers produced by primary cosmic rays. The method also enables stable and uniform triggering conditions to be achieved.