The spread of socially-learnt behaviours occurs in many animal species, and understanding how behaviours spread can provide novel insights into the causes and consequences of sociality. Within wild populations, behaviour spread is often assumed to occur as a "simple contagion". Yet, emerging evidence suggests behaviours may frequently spread as "complex contagions", and this holds significant ramifications for the modes and extent of transmission. We present a new framework enabling comprehensive examination of behavioural contagions by integrating social-learning strategies into network-based diffusion analyses. We show how our approach allows determination of the relationship between social bonds and behavioural transmission, identification of individual-level transmission rules, and examination of population-level social structure effects. We provide resources that allow general applications across diverse systems, and demonstrate how further study-specific developments can be made. Finally, we outline the new opportunities this framework facilitates, the conceptual contributions to understanding sociality, and its applications across fields.