How does a DEX actually work?

Could you please elaborate on the inner workings of a decentralized exchange, or DEX? How does it facilitate peer-to-peer trading of digital assets without relying on a central authority? What are the key mechanisms and protocols that enable secure and efficient transactions on a DEX? How do users interact with the platform, and how are their funds and transactions safeguarded? I'm particularly interested in understanding the technical aspects of how a DEX operates.