Group-living organisms that collectively migrate range from cells and bacteria to human crowds, and include swarms of insects, schools of fish, and flocks of birds or ungulates. Unveiling the behavioural and cognitive mechanisms by which these groups coordinate their movements is a challenging task. These mechanisms take place at the individual scale and can be described as a combination of interactions between individuals and interactions between these individuals and the physical obstacles in the environment. Thanks to the development of novel tracking techniques that provide large and accurate datasets, the main characteristics of individual and collective behavioural patterns can be quantified with an unprecedented level of precision. However, in a large number of studies, social interactions are usually described by force map methods that only have a limited capacity of explanation and prediction, being rarely suitable for a direct implementation in a concise and explicit mathematical model. Here, we present a general method to extract the interactions between individuals that are involved in the coordination of collective movements in groups of organisms. We then apply this method to characterize social interactions in two species of shoaling fish, the rummy-nose tetra (Hemigrammus rhodostomus) and the zebrafish (Danio rerio), which both present a burst-and-coast motion. From the detailed quantitative description of individual-level interactions, it is thus possible to develop a quantitative model of the emergent dynamics observed at the group level, whose predictions can be checked against experimental results. This method can be applied to a wide range of biological and social systems.