We review empirical methods that can be used to provide physical descriptions of dynamic cellular processes during development and disease. Our focus will be nonspatial descriptions and the inference of underlying interaction networks including cell-state lineages, gene regulatory networks, and molecular interactions in living cells. Our overarching questions are: How much can we learn from just observing? To what degree is it possible to infer causal and/or precise mathematical relationships from observations? We restrict ourselves to data sets arising from only observations, or experiments in which minimal perturbations have taken place to facilitate observation of the systems as they naturally occur. We discuss analysis perspectives in order from those offering the least descriptive power but requiring the least assumptions such as statistical associations. We end with those that are most descriptive, but require stricter assumptions and more previous knowledge of the systems such as causal inference and dynamical systems approaches. We hope to provide and encourage the use of a wide array of options for quantitative cell biologists to learn as much as possible from their observations at all stages of understanding of their system of interest. Finally, we provide our own recipe of how to empirically determine quantitative relationships and growth laws from live-cell microscopy data, the resultant predictions of which can then be verified with perturbation experiments. We also include an extended supplement that describes further inference algorithms and theory for the interested reader.