A strong background in zoology is necessary for most of the jobs that involve working closely with animals. Ask your school counselor to help you work out a course list that will prepare you to earn a degree in zoology, biology, chemistry, botany, or psychology. Take your classes seriously; zoological parks are more interested in hiring a hard-working, knowledgeable person than someone who "loves animals."
Don't wait until you have a degree before you apply for a job at a zoological park. Some of the curators, supervisors, aquarists, and others got their start by working at snack stands and gift shops before moving into their present careers. An entry-level position will help you establish a name for yourself as a dedicated employee, and introduces you to how hiring is handled within that zoological institution.
Lastly, many of the professional organizations listed in the Appendix have special membership rates for nonprofessionals and students. You'll be able to learn more about animals and zoological careers through their newsletters. Also, by attending local workshops and even national conferences, you might make some good contacts and get more information on how to chart your path for your zoological park career.