The Borg never create, they only assimilate. When a vessel or planet has caught the Borg's attention, they would sweep it with their sensors and then transport drones over to investigate the technology up close. If they deemed the vessel and its occupants worthy of assimilation, they would announce “We are the Borg. You will be assimilated. Your biological and technological distinctiveness will be added to our own. Resistance is futile.” They would then acquire the vessel by force and transform the occupants into drones, turning their bodies and minds entirely over to the Collective and its purposes.
Using nanoprobes, the Borg took control of their new drones at the cellular level, and later in the process, surgically attached larger, more complex cybernetic implants. Once fully assimilated, a drone would be devoid of its original persona, and function only at the will of the Collective.