There is much speculation as to how the Xenomorph Queen are born, many believe a royal facehugger implants a Queen embryo within its victim. It is stated that a Royal Facehugger can implant several victims before it dies, and this can be seen as the case for what occurred during the events of Alien 3.
Another possibility is the Queen Facehugger, which appeared as an action figure released by Kenner after Aliens. However, these are stated as only being created as a comparison between the Warriors and the Xenomorph Queen, and are therefore very likely non-canonlogical.
In the game Alien vs. Predator: Extinction, a Praetorian Facehugger can infect any host to make a praetorian then for numerous points evolve into a queen.
It may be possible for an ordinary facehugger to implant a Queen embryo in the absense of a Royal or a Praetorian Facehugger.