Research on the evolution of human speech and phonology benefits from the comparative approach: structural, spectral, and temporal features can be extracted and compared across species in an attempt to reconstruct the evolutionary history of human speech. Here we focus on analytical tools to measure and compare temporal structure in human speech and animal vocalizations. We introduce the reader to a range of statistical methods usable, on the one hand, to quantify rhythmic complexity in single vocalizations, and on the other hand, to compare rhythmic structure between multiple vocalizations. These methods include: time series analysis, distributional measures, variability metrics, Fourier transform, auto- and cross-correlation, phase portraits, and circular statistics. Using computer-generated data, we apply a range of techniques, walking the reader through the necessary software and its functions. We describe which techniques are most appropriate to test particular hypotheses on rhythmic structure, and provide possible interpretations of the tests. These techniques can be equally well applied to find rhythmic structure in gesture, movement, and any other behavior developing over time, when the research focus lies on its temporal structure. This introduction to quantitative techniques for rhythm and timing analysis will hopefully spur additional comparative research, and will produce comparable results across all disciplines working on the evolution of speech, ultimately advancing the field.