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?