It's not that different from how it currently works, but the difference is the platform is distributed and not centralized. NFTs are nonfungible, and the contract process guarantees the NFT can't be owned by multiple wallets. There can be only "one".
A venue generates 5000 NFTs (could be individual seats, could be general ticket) and puts them on an NFT marketplace (e.g. OpenSea) for the ticket price (e.g. $100) + 1% (OpenSea will also charge a fee). I buy one of those tickets for $101. I go to the venue. The ticket scanner sends a challenge to my phone, and my phone generates a signature that proves I have the ticket, and I go in.
If I can't go for whatever reason I can't go, I can post the NFT to the same or a different marketplace. Note that NFTs don't necessarily prevent ticket scalping, however because it's part of a digital contract you can also code an upper limit for the resale of the NFT which would definitely hurt scalpers. But just eliminating the vendor lock-in of the ticket exchange would cut fees between 95 and 99%.
Logistically, what if I lose my phone, and can't verify the challenge proving I have the NFT at the gate (or whatever similar scenario). The same system intended to prevent fraud also means the system is not flexible for human error. But maybe that's worth it for everyone to not have to pay 15-30% fees by centralized ticket management systems.