A great source for information about careers and research opportunities in the field is the Animal Behavior Society website. Researchers who need undergrad and grad student assistants often post in the ABS newsletter.
If you're interested in working directly with animals, an undergraduate degree is typically required (in psychology, zoology, or biology). If you want to do research with animals, you should consider graduate school. A Master's degree is the minimum standard for most occupations in this field.
If you're a psychology student, you are probably interested in how animals think! You should check out the Comparative Cognition Society for news, grad opportunities, and our annual Florida conference, which is really fun and the best place to learn about exciting research in this field.