In the US, they have to get an undergraduate degree in a science related field, then be accepted into veterinary school, which I believe is 4 years on average. After that they have to pass a licensing test through the American Veterinary Medical Association's (AVMA), and the state. So it is similar to getting a medical license, typically minus the extended residency programs. I know their veterinarians who have specialties, though I am not sure of the requirements of those.
There are no real specialties per animal in school. They have to go through rotations in animal hospitals somewhere in the last few years of school. Obviously once they start a practice they can specialize in whatever they want, or work with or under another vet who specializes in farm animals, reptiles, etc... But, at least in my experience, the vast majority start or work in a "Family practice" type of office, where 95% of what they do is treat cats and dogs.