Recent advances in computational infrastructure and large-scale data processing have accelerated the adoption of data-driven inference methods, particularly deep learning (DL), to solve problems in many scientific and engineering domains. In wireless systems, DL has been applied to problems where analytical modeling or optimization is difficult to formulate, relies on oversimplified assumptions, or becomes computationally intractable. However, conventional DL models are often regarded as non-transparent, as their internal reasoning mechanisms are difficult to interpret even when model parameters are fully accessible. This lack of transparency undermines trust and leads to three interrelated challenges: limited interpretability, weak generalization, and the absence of a principled framework for parameter tuning. Science-informed deep learning (ScIDL) has emerged as a promising paradigm to address these limitations by integrating scientific knowledge into deep learning pipelines. This integration enables more precise characterization of model behavior and provides clearer explanations of how and why DL models succeed or fail. Despite growing interest, the existing literature remains fragmented and lacks a unifying taxonomy. This tutorial presents a structured overview of ScIDL methods and their applications in wireless systems. We introduce a structured taxonomy that organizes the ScIDL landscape, present two representative case studies illustrating its use in challenging wireless problems, and discuss key challenges and open research directions. The pedagogical structure guides readers from foundational concepts to advanced applications, making the tutorial accessible to researchers in wireless communications without requiring prior expertise in AI.