Take courses through a private institute that offers training in applied animal behavior. While these courses are not usually accredited, they can give you a start as an animal behavioral specialist.
Take college courses in fields like animal behavior, zoology, psychology and pharmacology. If you are mainly interested in animal behavior research, you might want to get a PhD in animal behavior, or if you want to be a practitioner, you can go for a professional degree, for example in veterinary science.
Get credentialed through societies such as the Animal Behavior Society or the Certification Council for Professional Dog Trainers. You can apply for certification after getting the necessary college education in these fields as explained in Step 2. Such certifications will allow you to join professional bodies like the Association of Pet Dog Trainers, which will give you greater standing in your career.