The quantitative analysis of cell motility in culture has several important functions. First, it gives a concise and accurate description of the motile process and can detect subtle differences in motility due to different genetic makeup or experimental conditions. Second, its objectivity means that results can be communicated precisely and used unambiguously to test hypotheses about motility. Third, it may be used to derive a mathematical model with the same statistical properties as the motile process and thus elucidate the mechanism of motility. In this paper, we introduce a general procedure for analysing cell motility in a wide variety of circumstances. We describe a pilot project for the analysis of simple geometrical data obtained from randomly moving fibroblasts. Finally, as an example, we show how an analysis of the translocation of the fibroblasts can lead to insights into the mechanism of motility that are arguably not obtainable by any other approach.