How does dex swap work?

Excuse me, could you please explain how a decentralized exchange, or DEX, swap works in simple terms? I'm curious to know how users can trade cryptocurrencies without relying on a centralized authority like a traditional exchange. Is there a peer-to-peer system involved, and how does the process of matching buyers and sellers occur? Also, I've heard about smart contracts playing a role in DEX swaps. Could you elaborate on that aspect as well? Thank you in advance for your insights.