Usually a new small bee colony gets housed in a 4-frame or 5-frame nucleus hive, temporarily, a few weeks or months, as long as the bee colony is small.
To allow further growth of the colony the bees are then transferred into a single-box Langstroth starter hive, most commonly an 8-frame hive.
Once the 8 frames are fully developed and occupied by bees, usually a second 8-frame hive box (super) is stacked onto the hive, providing the bee colony with 16 frames.
A strong and healthy bee colony will run out of space in a two-tier beehive, so a third hive box with 8 frames gets stacked onto the hive, providing the colony with 24 frames to work on.
Very strong colonies will accept a 4th box; a better option though is to limit the number of boxes to three and instead replace frames full with honey by frames with wax foundation, providing the bees with the work space they need. It is different from colony to colony.
The most common question:
"How long does it take before I can add another super?"
Answer: It can take a few weeks, several months or more than a season. It all depends on the conditions: mostly on available food sources, but also weather, laying capacity of the queen and appropriate comb space to match laying capacity; too little space slows down brood raising capacity, too much space can result in chilling the brood during a cold weather snap leading to stress and fungus related brood diseases, such as Chalkbrood.