How do dexes work?

As a keen observer of the cryptocurrency market, I'm often curious about the intricate workings of decentralized exchanges, or dexes, as they've become a pivotal piece of the decentralized finance landscape. Could you elaborate on how dexes function and operate? Specifically, I'm interested in understanding the mechanisms behind order matching, liquidity provision, and the overall trading process. How do smart contracts play a role in enabling these exchanges to function without a centralized intermediary? Additionally, what are the key factors that contribute to the efficiency and liquidity of dexes? I'd appreciate a detailed yet concise explanation of these aspects to help me gain a deeper understanding of this fascinating aspect of the crypto world.