Cross-chain atomic swaps are a 100% secure and trust-less way to exchange bitcoin and Monero.
In contrast to BTC, XMR is a privacy-oriented network, you can send your BTC to XMR and transact there in a private way. You cannot protect your privacy using a third party to achieve this.
You use your own BTC and XMR addresses and you don’t need to convert to fiat first.
An exchange requires two parties, both with the special client that implements the mentioned protocol. While one part makes the offer, the other will find it and accept it. The protocol cryptographically provides means to make sure that no party can take advantage of the other one.