The queen bee lays eggs. Any egg can become one of the three kinds of bee.
Workers
Worker larva are fed brood food for six days. The nurse bees secrete brood food from their glands. Brood food is made when the nurse digests pollen and then secretes the nutrients out of her head.
Bee bread is made from pollen collected around bees legs. The collected pollen is given to the nurse bees. Extra pollen is packed into cells. Microbes digest and acidify this pollen, preserving it.
Drones
Are produced from eggs that are not fertilized (they only have 16 chromosomes, all from the mother)
Queens
Queen larva are fed “royal jelly” for four and a half days. Royal jelly is brood food with extra protein and extra sugar.
The first queen to emerge, kills the other queen which are still in the pupal state. She does this by nibbling on the queen cells. This tells the workers to tear down these queen cells.
If the first queen born does not kill all the other queens your hive will swarm twice. This is referred to as an "after-swarm".
It's True! The picture is of a brood frame. You can see the covered cells that currently contain pupae.