It depends on the particular aircraft, but presurization begins at takeoff (sometimes before sometimes right after), and the cabin climbs at a much slower rate than the actaul aircraft. While the aircraft might be climbing at 1,500 fpm, the cabin could would most likely be climbing at only 3-500 fpm. The systems logic used to regulate this vary greatly by aircraft, but it is [almost?] always an outflow vavlve that opens and closes to maintain the preasure that the copmuter wants.
When in doubt, one B pump off