Modern artificial intelligence systems, such as large language models, are increasingly powerful but also increasingly hard to understand. Recognizing this problem as analogous to the historical difficulties in understanding the human mind, we argue that methods developed in cognitive science can be useful for understanding large language models. We propose a framework for applying these methods based on the levels of analysis that David Marr proposed for studying information processing systems. By revisiting established cognitive science techniques relevant to each level and illustrating their potential to yield insights into the behavior and internal organization of large language models, we aim to provide a toolkit for making sense of these new kinds of minds.