Researchers face a critical choice: how to use -- or not use -- large language models in their work. Using them well requires understanding the mechanisms that shape what LLMs can and cannot do. This chapter makes LLMs comprehensible without requiring technical expertise, breaking down six essential components: pre-training data, tokenization and embeddings, transformer architecture, probabilistic generation, alignment, and agentic capabilities. Each component is analyzed through both technical foundations and research implications, identifying specific affordances and limitations. Rather than prescriptive guidance, the chapter develops a framework for reasoning critically about whether and how LLMs fit specific research needs, finally illustrated through an extended case study on simulating social media dynamics with LLM-based agents.