Matcha does not currently charge any platform fees. Making a trade does carry a small network fee + 0x protocol fee, both of which are necessary to process the transaction on the blockchain.
Network fees vary depending on the blockchain (e.g. Ethereum, Polygon, Celo, etc.) and will display at the bottom of the trading widget:
📚 Recommended reading to learn more Network fees and gas:
Ethereum Gas Explained in Plain English [Coinmonks]
What is Ethereum gas? [Blockgeeks]