Well, there are several ways, but how you go about it depends on what you were assigned to be when you arrived. You can get money from the trainers you battle, but most people get jobs in the different towns.

I am a breeder, and if I needed extra money I can sell the eggs I breed for a profit.

[Of course, thanks to Togami's moneycats, he doesn't have to do that.]

So it...really all depends on what you think you would feel most comfortable doing. Trainers can still breed, but they will not find as many eggs as quickly as a breeder would.