Well, this is rather convenient. Do you want do buy or to sell crypt? Actually, there's no difference the system is the same, anyway. Whoever wants to buy or sell the asset, places a bet (bid or offer) into the system. I saw Coinplace announcing hidden dashboards for bigger pool deals but here we're talking about the open part.
So, when there is a match between the two sides, i.e. buyer and seller, the deal is done. Technically, the one who has crypt on his/her hands, places it in a custody (escrow). And the other side transfers fiat. When fiat is received, the "crypt" side unlocks the escrow.
And what are the guarantees that I will receive crypto after transferring fiat?
It is locked in a decentralized custody. I.e., it's a smart contract that is delivering to you upon confirmation of the fiat payment. It is interesting to see what happens if the other side is commiting a fraud and tries to escape without paying. First, they won't be able to get the crypt back, second, there's an arbitrary board that may decide to unlock the pledge in case you provide sufficient proof that the payment took place (like receipt or like that).