Which ones are reliable?
If you ask for CEX then i will suggest you Binance & Kucoin but if you ask for DEX then you can use any popular dex, coz here your crypto will be in your control so the risk will be less.
Which ones are people actually using?
Must of the trader's are using Binance as a CEX and uniswap, pancakeswap and others DEX depending on blockchain.
How do they work?
Every CEX required deposit crypto and trade/exchange and withdraw but if you ask for DEX then here you have to connect your wallet by metamusk or any others wallet Dapp and swap your crypto. here your swapped crypto will automatically added on your personal wallet where you are holding your old coin.