But how do they do it?
When visibility drops below a certain threshold, airports (specifically those equipped with the necessary infrastructure) activate what are known as "Low Visibility Procedures" (LVP).
In short, ground traffic is significantly reduced to minimize the risk of collisions. Consequently, the number of takeoffs and landings is limited—they occur "one drop at a time." This is one of the main reasons for delays when there is fog at either your departure or destination airport.
Furthermore, while these procedures are active, only aircraft equipped with specific instrumentation and pilots with specialized training for low-visibility operations are authorized to operate.
Takeoff in the Fog
From a pilot's perspective, a low-visibility takeoff isn't much different from a normal one, aside from a few extra precautions to keep the aircraft centered on the runway during the takeoff roll. The runway, of course, must be equipped with high-intensity lighting systems that help the pilots stay oriented.
The Automatic Landing
Landing, however, is a different story. In these conditions, it is an entirely automatic maneuver executed by the aircraft’s onboard systems, guided by a signal from the ground (the ILS). The pilots' role shifts: they must monitor for any tiny anomaly that could compromise safety. They stand ready to take control, abort the maneuver to try again, or decide to divert to an airport with better weather conditions.
The aircraft systems that allow for an automatic landing are what we call "fail-operational". This means that even if one component fails, the maneuver can still be completed in total safety because there is at least one "backup" system that immediately takes over.
The higher the level of "redundancy" (the number of backup systems), the lower the visibility requirements. Some aircraft are authorized to operate with as little as 75–100 meters of visibility! Certain models can even perform an autoland with one engine inoperative.
Finally, you should know that all pilots practice these low-visibility procedures—along with all possible system failures—at least twice a year in a flight simulator.
DontWorryFlyHappy!