Honeybees belong to the group called Hymenoptera, or roughly membrane winged insects. Most if no all of these type of insects have sex determined not by a sex chromosome like humans, but by the level of ploidy of the individual. Diploid eggs become female bees, haploid (unfertiziled) eggs become males.
The queen can determine the ploidy of the egg (I'm not sure how, exactly, but she does). She measures the prepared cell with her forelegs, and deposits the appropriate egg for the cell -- diploid egg for worker cells and queen cells, haploid egg for drone cells.
Queens are fed royal jelly, a secretion of the sub parietal glands, I think, for their entire larval stage. Worker bees are fed royal jelly for a few days, and then "bee bread", resulting in smaller, non-fertile females. Drones are fed like workers, but being male develop differently, of course, and are in much larger cells.
Queen cells are built out during the larval stage and hang down from the comb or wherever else they are placed, often on the bottom of frames. They look remarkably like a peanut.
Peter