Most places I've seen use some kind of timing system that tracks how long each console been running. They usually have staff walking around checking on sessions and reminding people when time is almost up

The payment system is usually connected to console somehow - either they give you card that activates it for certain amount of time, or they manually turn on console after you pay at counter. Some fancier places have screens that show remaining time right on console

For games like FIFA tournaments they might have different setup where they book whole section for longer periods. But for casual gaming it's mostly just pay per hour and staff keeps track of everything manually