The authenticity part is straight forward: if token was minted from contract X then it is the real deal. This can be an issue for brand new projects. Bad actor

The authenticity part is straight forward: if token was minted from contract X then it is the real deal. This can be an issue for brand new projects. Bad actors will duplicate it and list at low prices. Most users are savvy enough to only use links from a trusted source. Marketplaces also whitelist the real contract (and show warnings for unverified contracts). You can also look at the contract deployers wallet history to help determine if it is legit. IMO it’s easier to prove authenticity for NFTs than most stuff