What patandchickens said +1.
You need a perfect 4.0 in heavy-duty science classes. You need lots of volunteer experience, with cats & dogs AND with exotics AND with large farm animals such as cattle. Some students now do a 5 year undergrad Master's program to improve their chances. The pre-vet students I used to get argued over, literally, every single exam question they ever got wrong. The numbers game is insane. It's easier to get into human medical school, for sure.
The owners are insane, so you have to think of it like you'd think of being a pediatrician--crazed, frantic, not-as-helpful-as-you'd-like owners, who neglect to tell you that dear old Spot ate ten pounds of chocolate before going into shock and nearly dying. On the plus side, there's not really much they can do in case of malpractice, so I guess it has that over pediatrics.
I'm sure it's lots of fun for those who love it. I know my vet nearly poops his pants with glee whenever I bring the puppies in for their checkups, he calls the whole staff in to admire the housewolves. But a lot of down sides, too. A big part of the job is putting critters to sleep, sometimes for no better reason than the owner is too cheap to treat the animal's illness.