For depositing/withdrawing fiat you will need to do KYC on fiat gateways that will be integrated. While depositing your fiat will be converted to proper fiat token. Next you can trade it for Waves token and other currencies, assets supported on the platform. For trading crypto only and trading fiat tokens only without depositing/withdrawing fiat on the platform no KYC needed. Waves fiat tokens will be also integrated in Mycelium wallet.
Please correct if I'm wrong: there will be special gateways that are "official" partners and they are expected to be the most trustworthy ones. At the same time anyone can create a gateway since (unlike Ripple) Wave is a fully decentralized blockchain. So it's up to the users to make due diligence in order to avoid scammers. The reputation system will help and I expect to see the emergence of rating services.