If you are truly committed to zoo medicine then I would recommend trying to go the vet school > rotating internship > zoo internship > zoo residency route. And I'm not sure what experiences you've had, but I'd strongly recommend getting experience in the field before plotting out your career (same goes for all aspects of vet med). A lot of people think it sounds really cool but it's not for everyone.
Anyway, like hai1983 said the certification examination is taken after completing a residency (or after 6 years of full-time professional training/experience in zoo medicine). I'd take a look at the ACZM's website; all of the eligibility requirements for certification, programs, etc. can be found there.
With wildlife medicine (rehabilitation) you have basically the same limitations as you do with zoo medicine -- number of facilities. In my experience most wildlife rehabilitation centers don't have full-time veterinarians; they have a working relationship with an area veterinarian (or veterinarians) and consult as needed. Offhand, other wildlife medicine careers include becoming a state wildlife veterinarian (you'd have a lot more involvement in conservation, population management, disease surveillance, etc.) and working at the federal level. If you're into conservation biology then you could also consider international work vs. zoo medicine.
Also, you need to have a demonstrated interest in the field for either zoo or wildlife medicine. So undergraduate internships, shadowing, joining AAZV and AAWV once you're in veterinary school, becoming involved in your school's zoo/wildlife club, attending association meetings, wetlabs, multiple clinical rotations at zoos +/- wildlife facilities, etc.