It will depend on the zoo but typically to begin working in a zoo you start volunteering and this can be done as early as 10 years old in some states. It will also depend on where you want to work in the zoo as there are many different programs and career opportunities within a zoo. This ranges from event coordinators, human resources, tour guide etc. The older you are the more responsibilities and projects you can take on. Typically if you want to work with animals in a paid position it will require college course work in zoology to start. However if you start volunteering, the younger the better your chances of getting a paid job working with animals is greatly improved. I will warn you this field is extremely competitive and is why I recommend volunteering if you can to get your foot in the door.