Education within the Pokémon world probably doesn't deviate too much from education in the real world. The usage of Pokémon within the Pokémon world appears to vary between a career choice, as tools, or as a hobby, at least from what I've experienced from the games.
For example, there are various people who have "actual" jobs that just use Pokémon to battle for fun or help around the workplace - you can see this when you fight officers, scientists, fishermen, sailors... And I'm sure there are many others I'm forgetting. These people keep the world in balance by doing the normal jobs - after all, someone's gotta do them!
In addition, you can often battle children who are enrolled in school, and they'll often comment on their courses. One schoolboy outside of Fuschia City notes that "If Pokémon were a subject in school, I'd be the best!" (or something along those lines). This means some schools don't even teach Pokémon as a course - it seems to be something they have the option of getting involved in or not, much like sports or any other optional activity in this world. However, there are schools that teach Pokémon-related courses, so it's just a matter of which school you attend.
So... To sum up what I said: Education is probably similar to the real world, with Pokémon Training / Breeding / Whatever being one of the many career choices one could make.