Do airliners start changing cabin pressure at takeoff or after reaching a certain altitude? Also when do they start depressurizing the cabin ?
The cabin pressure is maintained automatically by a controller. Before the flight, the pilots will input two numbers: the cruise altitude and destination airport altitude. From these two inputs, the controller will manage the cabin pressure schedule automatically.
From the Boeing 737 FCOM:
The cabin begins to pressurize on the ground at higher power settings. (...)
In the air, the auto controller maintains a proportional pressure differential between airplane and cabin altitude. (...)
The descent mode is activated when the airplane descends 0.25 psi below the selected FLT ALT. The cabin begins a proportional descent to slightly below the selected LAND ALT. (...)
While taxiing in, the controller drives the outflow valve slowly to the full open position depressurizing the cabin.
For passenger comfort, the controller is programmed so that the rate of cabin pressure change is kept to a minimum. The cabin is actually slightly pressurized on the ground both during takeoff and landing, i.e. the cabin altitude is lower can the outside altitude. It smoothly transitions to and from cruise cabin pressure as the plane climbs or descends.