Cabin pressure is typically regulated from the moment power is set for takeoff
(on the runway), where cabin altitude goes slightly below the runway elevation. As the aircraft climbs, the cabin altitude is climbed at a proportional rate respecting passenger comfort and aircraft design limits.
On the older aircraft types, a pilot or flight engineer would set the planned cruise altitude during the preflight setup. When the plane gets to that altitude, pressurization would go into cruise mode, keeping the altitude steady even if the aircraft makes slight moves above and below the associated flight (pressure) altitude. On newer aircraft, the pressurization system would get the planned cruise altitude from the flight management computer.
Before descent, on older planes, the landing airport elevation would need to be set. As you may expect, modern planes would get landing field elevation from the FMC.
The pressurization system would recognize movement away from the cruising level, and if the movement is a descent, would switch into a mode proportionally reducing the cabin altitude as the aircraft makes its way down to land. Ideally, the cabin altitude at touchdown would be slightly below the runway elevation, then gradually equalize during the landing rollout.
This is a simplified version of airliner pressurization. Things can become more complicated, as when the flight never arrives at the planned cruise altitude or diverts to a field with a different elevation from the planned destination.
(grin) I once flew a turboprop with overpressure protection based on spring loaded outflow valves. If you climbed above the altitude corresponding to the max internal / external differential, cabin pressure would crudely push open those spring loaded valves and the result was wild "pressure bumps." Instead of a nice 500 to 1000 fpm change in cabin alt, it would be a sudden and uncomfortable 1500 fpm or more.